WILL MARK BRAINLIEST! please help with easy geometry problem!! :) and give explanation and steps too
Answers
Therefore , the solution to the given problem of triangle comes out to be x =20 degree and y = 20 degree.
Defining a triangleIn a plane, any three points can be joined to form triangles, that have 3 components and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.
Here,
Given : 140 degree
Since it is a scalar triangle
two sides will have equal angle,
Thus ,
x=y
=> x+ x + 140 =180
=> 2x = 180-140
=> 2x =40
=> x =20
Therefore , the solution to the given problem of triangle comes out to be
x =20 degree and y = 20 degree.
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Related Questions
*8th Grade practicing 9th Grade courses for regents*
Question:
4x + 8y = 20
-4x = 2y = -30
Type of Math: System of Equations (elimination)
What I would like to know, is the positive 4x in the top equation and the negative 4x in the bottom equation a zero pair? Thanks in advance!
Answers
The solution to the system of equation shown is (7, -1)
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The standard linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Given the equation:
4x + 8y = 20 (1)
-4x + 2y = -30 (2)
Solving by elimination method. Add equation 2 and 1:
10y = -10
y = -1
Put y = -1 in eqn 1:
4x + 8(-1) = 20
4x - 8 = 20
4x = 28
x = 7
The solution is (7, -1)
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The city of Montgomery collects 4 times more tons of plastic than tons of glass in their recycling program.the city collected 80 tons of glass in june.how much plastic did the city collect in June?
Answers
According to the information, it can be inferred that the city of Montgomery collected 320 tons of plastic in the month of June.
How to calculate how many tons of plastic the city collected in June?To calculate how many tons of plastic the city collected in June we must take into account the following information.
The city of Montgomery collects 4 times more tons of plastic than tons of glass in their recycling program.the city collected 80 tons of glass in june.Taking this information as a reference, we must perform the following operation to find the amount of plastic that Montgomery collected in June:
80 * 4 = 320So, the city of Montgomery collected 320 tons of trash in the month of June.
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which travels faster: a car that travels 6 miles in 10 minutes at a constant speed, or a train that travels 6 miles in 8 minutes at a constant speed? Explain how you know.
Answers
Both the car and the train are traveling at the same speed because they both cover the same distance in different amounts of time.
How does this happen?In this scenario,
the car is traveling at a speed of 0.6 miles per minute
and the train is traveling at a speed of 0.75 miles per minute.
Therefore, both are traveling at the same speed of 6 miles in 10 minutes or 6 miles in 8 minutes.
With this in mind, it can be seen that they both travel at the same speed and none is faster.
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Please answer this for me. It's missing, please answer asap.
Answers
Answer:
40
Step-by-step explanation:
This is an example of a composite function. And, in order to answer the given problem, we need to calculate first the inner function.
In this example, we have:
[tex]f(x) = x^{2} - 3x + 6\\g(x) = 5x - 10[/tex]
And, we are tasked to calculate the [tex]g(f(-4))[/tex]. Let's calculate first the [tex]f(-4)[/tex].
[tex]f(x) = x^{2} + 3x + 6\\f(-4) = (-4)^{2} + 3(-4) + 6\\f(-4) = 16 - 12 + 6\\f(-4) = 4 + 6\\f(-4) = 10[/tex]
Let's substitute this value to the function of g to get the final answer.
[tex]g(x) = 5x - 10\\g(f(-4)) = 5(10) - 10\\g(f(-4)) = 50 - 10\\g(f(-4)) = 40[/tex]
Thus, the final answer was 40.
Classify AABC by its sides. Then determine whether it is a right triangle,
A(6, 6), B(9, 3), C(2, 2)
Answers
The triangle ABC seems to be an scalene triangle since all of the sides AB, BC and CA have different lengths, and also the triangle is not a right angled triangle.
What is a scalene Triangle?A scalene triangle is a type of triangle in which all three sides have different lengths. In other words, none of its sides are of equal length. As a result, all three angles in a scalene triangle are also different. It is different from an Isosceles triangle, where at least two sides are of equal length and an equilateral triangle where all sides are of equal length.
What is a right angled triangle?A right triangle is a type of triangle in which one angle is a right angle (90 degrees). This makes it different from other types of triangles such as acute triangle and obtuse triangle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. This theorem is used to determine if a triangle is a right triangle or not.
The triangle ABC is a scalene triangle, as its sides have different lengths.
To determine whether it is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
To find the side lengths, we can use the distance formula, which is
d = √((x2 - x1)² + (y2 - y1)²)
AB = √((9 - 6)² + (3 - 6)²) = √(3² + (-3)²) = √18 = 3√2
BC = √((9 - 2)² + (3 - 2)²) = √(7² + 1²) = √50 = 5√2
AC = √((2 - 6)² + (2 - 6)²) = √(4² + 4²) = √32 = 4√2
We know that in a right triangle, one of the side should be the hypotenuse and the other two should be the legs. We can check if any one of the side is satisfying that. But in this case, we can see that none of the sides are satisfying that condition, therefore the triangle ABC is not a right triangle.
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ALL THE FOURTH GRADERS IN A CERTAIN ELEMENTARY SCHOOL TOOK A STANDARDIZED TEST. A TOTAL OF 85% OF THE STUDENTS WERE FOUND TO BE PROFICIENT IN READING, 78% WERE FOUND TO BE PROFICIENT IN MATHEMATICS, AND 65% WERE FOUND TO BE PROFICIENT INN BOTH READING AND MATHEMATICS. A STUDENT IS CHOSEN AT RANDOM.
1) WHAT IS THE PROBABILITY THAT THE STUDENT IS PROFICIENT IN MATHEMATICS BUT NOT READING?
2)WHAT IS THE PROBABILITY THAT THE STUDENT IS PROFICIENT IN READING BUT NOT MATHEMATICS?
3) WHAT IS THE PROBABILITY THAT THE STUDENT IS PROFICIENT IN BOTH?
Answers
1 . The following formula can be used to determine the likelihood that a pupil is proficient in arithmetic but not reading:
P(math proficient and not reading proficient) = P(math proficient) - P(math and reading proficient)
We are aware that 65% of kids are fluent in both reading and mathematics, and 78% of children are proficient in arithmetic.
So, the probability that a student is proficient in mathematics but not reading is:
78% - 65% = 13%.
2 . The following formula can be used to determine the likelihood that a pupil is proficient in reading but not mathematics:
P(reading proficient and not math proficient) = P(reading proficient) - P(math and reading proficient)
We are aware that 65% of children are proficient in both reading and mathematics, and 85% of pupils are proficient readers. So, the probability that a student is proficient in reading but not mathematics is:
85% - 65% = 20%.
3 . The formula P(math and reading proficient) = P(math proficient) + P(reading proficient) - P can be used to determine the likelihood that a student is proficient in both reading and math (math proficient or reading proficient)
We are aware that 78% of pupils demonstrate arithmetic proficiency, 85% demonstrate reading proficiency, and 65% demonstrate reading and math proficiency. Therefore, there is a 65% chance that a student will be proficient in both reading and mathematics.
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The probability that a student is proficient in mathematics but not reading is 13%. The probability that a student is proficient in reading but not mathematics is 20%.There is a 65% chance that a student will be proficient in both reading and mathematics.
1 . The following formula can be used to determine the likelihood that a pupil is proficient in arithmetic but not reading:
P(math proficient and not reading proficient) = P(math proficient) - P(math and reading proficient)
We are aware that 65% of kids are fluent in both reading and mathematics, and 78% of children are proficient in arithmetic.
So, the probability that a student is proficient in mathematics but not reading is:
78% - 65% = 13%.
2 . The following formula can be used to determine the likelihood that a pupil is proficient in reading but not mathematics:
P(reading proficient and not math proficient) = P(reading proficient) - P(math and reading proficient)
We are aware that 65% of children are proficient in both reading and mathematics, and 85% of pupils are proficient readers. So, the probability that a student is proficient in reading but not mathematics is:
85% - 65% = 20%.
3 . The formula P(math and reading proficient) = P(math proficient) + P(reading proficient) - P can be used to determine the likelihood that a student is proficient in both reading and math (math proficient or reading proficient)
We are aware that 78% of pupils demonstrate arithmetic proficiency, 85% demonstrate reading proficiency, and 65% demonstrate reading and math proficiency. Therefore, there is a 65% chance that a student will be proficient in both reading and mathematics.
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MATHEMATICAL
CONNECTIONS Which
pairs of coordinates
represent the endpoints of
a line segment whose
midpoint is the origin?
O (m, 0) and (m, 0)
Ok, h) and (k, h)
O (a, b) and (a, b)
O (-k, 0) and (0, k)
O (0, - k) and (0, k)
Answers
Answer:
(m,0) and (m,0),(-a,-b) and (a,b),(0,-k) and (0,k) are the required coordinates
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Calculator
The observation deck of the Willis Tower in Chicago is 412 meters above the ground. On a scale drawing, this distance is 82.4
centimeters. The actual height of the building itself is 442 meters.
What is the height of Willis Tower in the scale drawing?
O 5.4 centimeters
O 76.8 centimeters
O 88.4 centimeters
O 112.4 centimeters
A
2 3
4
5
Finish
Answers
In the scale drawing, the height of building itself is 88 .4 centimeters.
What is scale drawing?
The scale drawing is a smaller edition of a large object. By using scale drawing we try to bring the large shape of image or any object within a sheet of paper or in a computer screen. The ratio of the dimension of scale drawing to the original dimension is called scale factor.
What is the height of Wills Tower in the scale drawing?
The height of observation deck of the Wills tower from ground surface = 412 meters
in the scale drawing the height of deck = 82.4 centimeters.
The actual height of Wills tower building = 442 meters
now, the height of Tower building in scale drawing = (442×82.4) / 412
in the scale drawing the height = 88.4 centimeters
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for what values of k will the line be tangent to the circle ?x^2 + y^2 = 25 where y = x+k.please help I have an exam tomorrow
Answers
Answer: To find the values of k for which the line y = x + k is tangent to the circle x^2 + y^2 = 25, we need to substitute y = x + k into the equation of the circle and solve for x.
x^2 + (x + k)^2 = 25
Expanding the square, we get:
x^2 + x^2 + 2xk + k^2 = 25
2x^2 + 2xk + k^2 = 0
Now we can solve for x by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 2, b = 2k and c = k^2
x = (-2k ± √(4k^2 - 42k^2)) / 2*2
x = (-k ± √(-3k^2)) / 4
Since the square root of a negative number is not a real number, we can see that there is no real value of x that will make the equation true. Therefore, the line y = x + k is never tangent to the circle x^2 + y^2 = 25
Answer:
Step-by-step explanation:
To find the values of k that will make the line y = x + k tangent to the circle x^2 + y^2 = 25, we need to set the equation of the line equal to the equation of the circle and solve for k.
First, we'll substitute y = x + k into the equation of the circle:
x^2 + (x + k)^2 = 25
Next, we'll expand the square on x + k:
x^2 + x^2 + 2xk + k^2 = 25
Now we'll combine like terms:
2x^2 + 2xk + k^2 = 25
We'll rearrange the equation so that x^2 is on one side
2x^2 + 2xk + k^2 - 25 = 0
Now we'll divide by 2
x^2 + xk + k^2/2 - 25/2 = 0
Now we'll complete the square
x^2 + xk + (k^2/2 - 25/2) = 0
x^2 + xk + (k^2/2 - 25/2) + (25/2) = (25/2)
(x + k/2)^2 = 25/2
Now we'll take the square root of both sides
x + k/2 = +-sqrt(25/2)
Now we'll solve for x
x = sqrt(25/2) - k/2 or x = -sqrt(25/2) - k/2
Now we'll substitute these values of x into the equation y = x + k and find the value of k.
x = sqrt(25/2) - k/2
y = x + k
y = sqrt(25/2) - k/2 + k
y = sqrt(25/2)
x = -sqrt(25/2) - k/2
y = x + k
y = -sqrt(25/2) - k/2 + k
y = -sqrt(25/2)
So the line y = x + k is tangent to the circle x^2 + y^2 = 25 when k = sqrt(25/2) or k = -sqrt(25/2)
Which of the following functions is graphed below?
Answers
Answer: it's a function
Step-by-step explanation:
Determine the length of AB (round your answer to the nearest whole number)?
Answers
Answer:
AB ≈ 13 cm
Step-by-step explanation:
∠ CAB = 90° - ∠ CAD = 90° - 45° = 45°
using the cosine ration in right triangle ABC
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{9}{AB}[/tex] ( multiply both sides by AB )
AB × cos45° = 9 ( divide both sides by cos 45° )
AB = [tex]\frac{9}{cos45}[/tex] ≈ 13 cm ( to the nearest whole number )
Let f be the function given by f(x) = tan x and let g be the function given by g(x) = x³. At
what value of x in the interval 0 ≤x≤ pi do the graphs of f and g have parallel tangent lines?
Answers
The value of x in the interval 0 ≤x≤ pi is 2.083 so the graph f and g have parallel tangent lines
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = tan x
and, g(x) = x²
Now, f(x) = t g(x)
and, g(x) = x²
On differentiating f(x) we get
f'(x) = t g²(x) + 1
and, g(x) = 2x
Now, the parallel tangent line
f' (x) = g'(x)
t g²(x) + 1 = 2x
since the interval for x is 0 ≤x≤ pi.
So, the value of x = 2.083
Hence, the value of x is 2.083.
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Determine if the equations are parallel, perpendicular, or neither. 2y=-3x = 6 and y = -3/2x + 5
Answers
You can use the formula y=mx+b, where m is the slope.
Your gradient is -3/2.
What are Equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
A statement is not an equation if it has no "equal to" sign.
According to our question-
y=-3/2x+1
Your slope in the second equation is -3/2 since y=-3/2x+5 is already in the form y=mx+b and m is the slope.
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63.8 x 4.6
show your work ;)
Answers
Therefore, by simply multiplying 63.8 by 4.6, we get 293.48. Once you have mastered each times table, move on to the next one.
what is multiplication ?The quantity of items in the group expands as we multiply. Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. In the first and second grades, students learn how to represent, work out, and extend their counting sequences. Students start learning basic multiplication facts and times tables in the third grade.
given
Slice up the information into manageable pieces. With a straightforward picture, give the facts context. Teach your kid how to use the simpler facts as stepping stones for the more difficult ones. Once you have mastered each times table, move on to the next one.
63.8 x 4.6
by simple multiplication
= 293.48
Therefore, by simply multiplying 63.8 by 4.6, we get 293.48.
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What special names are there for this quadrilateral?
Select all that apply.
A quadrilateral has two pairs of opposite sides and four right angles. The opposite sides are parallel and equal in length, but the adjacent sides are not the same length.
A.
rectangle
B.
square
C.
parallelogram
D.
trapezoid
Answers
Answer:
A. rectangle------------------------------
A. rectangle
Yes, it has all the mentioned properties.B. square
No, it has four equal sides.C. parallelogram
No, it doesn't have 4 right angles.D. trapezoid
No, it doesn't have 4 right angles, only one pair of parallel sides of different length.A music streaming service charges $7 per month for the first user, and $4 more per month for each additional user. Which function represents the monthly bill y in terms of the number of additional users x ?
Answers
The function for the monthly bill can be written as y = 7 + 4x.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a music streaming service charges $7 per month for the first user and $4 more per month for each additional user.
The equation can be written as,
y = 4x + 7
Here, y is the monthly charge and x is the number of months.
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what does GCF stand for?
Answers
Answer:
Greatest Common Factor
Step-by-step explanation:
Answer:
greatest common factor
Step-by-step explanation:
Find x and find the angle of M
Answers
Answer:
Step-by-step explanation:
well first you must question what 11 minus 9 is and its the x for m but do the same for o and combine the 2. i don't know if it will work i'm so past that
Algebra 2 big ideas math please help me
Answers
Answer:
Step-by-step explanation:
9
for the following function: g=2x-10 find g(20)
Answers
Answer:
-20 beacause - x + = - and you do 2x10
Pam has 125 gummy bears. Bob has 87 more than Pam. How many gummy bears does Bob Have?
Answers
Answer:
212 gummy bears
Step-by-step explanation:
Just add 125 and 87 together
Answer: 212
Step-by-step explanation:
Its simple addition.
Subtract 3x² + 7x - 4 from
8x² - 6x + 2.
standard form
Answers
On subtracting 3x² + 7x - 4 from 8x² - 6x + 2, the expression in standard form is obtained as 5x² - 13x + 6.
What is standard form?
To make mathematics easier for everyone to read, write, and work with, mathematicians from all around the world resolved to come to basic writing standards. The term "standard form" refers to this particular method.
The given expressions are -
a = 3x² + 7x - 4 and b = 8x² - 6x + 2.
Subtract a from b. The expression will be -
= (8x² - 6x + 2) - (3x² + 7x - 4)
= 8x² - 6x + 2 - 3x² - 7x + 4
= 5x² - 13x + 6
Therefore, the standard form is 5x² - 13x + 6.
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100 POINT!
Explain the mistake of this problem.
(the top is the real problem and the bottom 2 lines is them simplifying it.) (I'm pretty sure you're finding out the mistake in them simplifying.
Answers
Answer:
- 18 - 2√3-------------------------------
See the correct solution below:
(2 + 2√3)(3 - 4√3) = 6 - 8√3 + 6√3 - 8√9 = The mistake was at this step6 - 2√3 - 8*3 = Also not considered √9 = 3 6 - 2√3 - 24 = - 18 - 2√3Complete the table below, indicating what percentage of your overall course grade is taken from each course component:
In-Class Participation: 2 % (we'll assume this to be true for this question, though it might be different for your section)
Graded Homework in WebAssign: 23
%
Midterm Tests (total for three tests): 50
Final Exam: 25
%
%
Let's assume that you earn 100% for your In-Class Participation score, 91% for your Graded Homework score 95%.on.Test 1,
81% on Test 2, 97% on Test 3, and 86% on the Final Exam. What would your overall course grade be?
x
Enter a number.
Answers
The ultimate grade for the course is determined by the average of all completed assignments. Answer is 92.
What would be the final grade for the course?You must first add up all of your grades if your instructor or professor employs a total points system.Afterward, tally the number of points available for each of those grades.
Your class grade can be calculated by dividing your earned points by the total points available.Follow these steps if you want to accomplish it by hand:The letter grade's value is calculated by dividing it by the course's total number of credits.Do this for each class, then add them all up.
Subtract the total by the number of credits.
75% of the test score would be 76 x 0.75 = 57
80-57 = 23
They need 23 more points to get an 80
The 23 is 25% of the final exam grade so they would need to score a 23 x 4 = 92 on the final exam
answer: 92
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elise is a project manager
Answers
Elise average pay per hour in 2017 is 13.73 pounds
How to calculate the average pay?Elise earned 2100 as a monthly salary in 2016.In 2017, she got a 3% pay increase on her monthly salary.
So, in 2017 she got a monthly salary of (1+3/100)*2100= 2163
Then her yearly salary in the year 2017 became (2163 × 12) =25956
In 2017, Elise worked for 1890hours.
Therefore, her average pay per hour for the year 2017 will be:
= 25956 / 1890
= 13.73
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Complete question
in 2016, she earned a monthly salary of £2100
In 2017, she earned a 3% pay increase on her monthly salary.
Given that in 2017 Elise worked 42 hours per week for 45 weeks work out her average pay per hour for the year.
7x^2-10=-17 solve by taking square root
Answers
Step-by-step explanation:
[tex]7x^2-10=-17\\7x^2=-7\\x^2=-1\\x=\sqrt{-1}\\x=\sqrt{i^2}\\\boxed{x=i,-i}[/tex]
Phil and Meredith work for a book publisher editing mathematics textbooks. Phil has less experience and takes four times as long as Meredith to edit a textbook. Together, it takes them 16 hours to edit a textbook.
How long does it take Phil to edit a textbook if he works alone?
How long does it ake Meredith to edit a textbook if she works alone?
Answers
Let x be the time (in hours) it takes Meredith to edit a textbook alone. We know that Phil takes 4x hours to edit a textbook alone, since he takes four times as long as Meredith.
We also know that it takes them 16 hours to edit a textbook together. We can use this information to set up the equation:
x + 4x = 16
5x = 16
x = 16/5
So it takes Meredith 16/5 hours to edit a textbook alone.
We know that Phil takes 4x to edit a textbook alone, so we can substitute in the value we found for x to find his time:
4x = 4(16/5) = 16/5 * 4 = 64/5
So it takes Phil 64/5 hours to edit a textbook alone.
Sam has 26 seashells.
He collects 31 more seashells.
• Then he gives 14 seashells away.
Which equation shows the number of seashells, s, Sam has now?
Answers
Answer:
hshs7hhs7bs7bs8be8
Step-by-step explanation:
26+31= 57-14=43
Answer:
26+31-14
Step-by-step explanation:
using pendant you should answer that correctly so...
26+31=57-14 and you should get 43
in written form...
Sam has 31 seashells to his 26 seashells giving him the total of 57. Sam then gave away 14 of the 57 seashells away leaving him with 43 seashells.
hope this helps
Paula lives 1 9/10miles from school. Nate lives 1 3/4 miles from school. Cristian lives 11/8 miles from school. Who lives closest to school?
Answers
Cristian lives closest to school in linear equation.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Paula = 1 9/10miles
Nate = 1 3/4 miles
Cristian = 11/8 miles
Paula = 19/10
Nate = 7/4
Cristian = 11/8
now take LCM
Total distance from school is 40 miles
Paula = 19/10 * 40 = 76
Nate = 7/4 * 40 = 70
Cristian = 11/8 * 40 = 55
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( 100 pts) very urgent please ASAP. Prove that the points (-3, 3), (3, -7) and (7,9) are the vertices of a right angled isosceles triangle.
Answers
A right angled isosceles triangle is a triangle with two sides of equal length and one right angle. To prove that the points (-3, 3), (3, -7) and (7,9) are the vertices of a right angled isosceles triangle, we can use the distance formula and the Pythagorean theorem.
The distance formula is used to calculate the distance between two points in a coordinate plane. It is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the distance formula, we can find that the distance between the points (-3, 3) and (3, -7) is:
d = √((3 - (-3))^2 + ((-7) - 3)^2) = √(6^2 + (-10)^2) = √(36 + 100) = √136
Similarly, we can find that the distance between the points (-3, 3) and (7, 9) is also √136 and the distance between the points (3, -7) and (7, 9) is √36.
Now, we can use the Pythagorean theorem, which states that in a right angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2
Since d1 and d2 are equal, we can say that the triangle is isosceles.
So, using the distance formula and the Pythagorean theorem, we have proven that the points (-3, 3), (3, -7) and (7,9) are the vertices of a right angled isosceles triangle.