Mathematics High School

When a point is reflected across a line of reflection, it remains the same distance from the line.True or False

Answers

Answer 1

Answer:

True

Step-by-step explanation:

To answer this question, I will use the following illustrations.

Assume a point (x,y) is reflected across the x-axis.

Using reflection rule, the new point will be: (x,-y)

On a coordinate plane, the x-axis is represented as: (x,0)

So, we will calculate the distance between (x,y) and (x,0) and also calculate the distance between (x,-y) and (x,0) using the following distance formula.

[tex]D= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Distance between (x,y) and (x,0)

[tex]D= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]D= \sqrt{(x - x)^2 + (0 - y)^2}[/tex]

[tex]D= \sqrt{(0)^2 + (- y)^2}[/tex]

[tex]D= \sqrt{0 + y^2}[/tex]

[tex]D= \sqrt{y^2}[/tex]

[tex]D = y[/tex]

Distance between (x,-y) and (x,0)

[tex]D= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

[tex]D= \sqrt{(x - x)^2 + (0 - (-y))^2}[/tex]

[tex]D= \sqrt{(0)^2 + (0+y)^2}[/tex]

[tex]D= \sqrt{0 + y^2}[/tex]

[tex]D= \sqrt{y^2}[/tex]

[tex]D = y[/tex]

See that the calculated distance are equal.

Hence, the given statement is true

Related Questions

8.

Find the slope of the line.

A. 0
B. -2
C. Undefined
D. 2

Answers

Answer:

C. Undefined

Step-by-step explanation:

Input Data :

Point A

(

)

= (2, 5)

Point B

(

)

= (2, -2)

Objective :

Find the slope of a line that passes through points A and B.

Formula :

Slope

−

Solution:

Slope

−

m = -INF

Answer:

The answer is C (Undefined)

Step-by-step explanation:

A vertical slope is undefined because it rises and never runs up/down is rise and left/right is run. Rise/Run. 4/0. Four divided by zero is undefined while 0 divided by 4 is zero.

Find the sum:
15.07 +22.8
a. 37.01
b. 37.1
c.37.87
d. 37.78

Answers

The answer is : C. 37.87

What is the slope of the line?
y + 2 = -2 ( x - 3 )
A: -1/2
B: -2
C: 1
D: -1

Answers

D:) o b what ? you very whell

Step-by-step explanation:

A b. d. c

Answer:

The answer is -2

Step-by-step explanation:

I got this answer on Khan Academy.

Hope this helps! :)

How do I factor -2y+2y^2-24

Answers

Well this is a quadratic equation so.
First we rearrange it
2y^2-2y-24
2y^2-2y-48
2y^2-8y+6y-24
2y(y-4)+6(y-4)
(2y+6)(y-4)

2(y ^2-13) is it factored

what is the factored form of 3/4(24x + 28) - (4x - 1)?

Answers

Answer:

2(7x + 11)

Step-by-step explanation:

3/4 ( 24x + 28) - (4x - 1) = 18x + 21 - 4x + 1 = 14x + 22 = 2(7x + 11)

Answer:

2(7x + 11)

Step-by-step explanation:

3/4 (24x + 28) - (4x - 1)

= 18x + 21 - 4x + 1

= 14x + 22

= 2(7x + 11)

Please give me brianliest and follow me if you want me to help you always

Someone plz help me I will give brainliest

Answers

Answer:

Step-by-step explanation:

5. 3/4 +3/4 + 3/4 + 3/4 + 3/4 + 3/4 = (6 x 3)/4 = 18/4 = 4 1/2

6. 16 x 3 x 1/8 = (48x 1)/8 = 48/8 = 6

7. 500 x 2/5 = 500 x 2 x 1/5 = (1000 x 1)/5 = 1000/5 = 200

Factor completely by grouping: 6x² + 2x + 9x +3
is

Answers

Answer:

(2x+3)(x+1)

Step-by-step explanation:

6x² + 2x + 9x +3

(6x² + 2x) + (9x +3)

2x (x+1) + 3 (x+1)

(2x+3)(x+1)

Answer:

(3x+1) ( 2x+3)

Step-by-step explanation:

6x² + 2x + 9x +3

Make the groups

6x² + 2x + 9x +3

Factor 2x out of the first group and 3 out of the second group

2x( 3x+1) + 3(3 x+1)

Now factor out the common term inside the parentheses

(3x+1) ( 2x+3)

Harry got a raise. He now makes 105% of his old salary.
If his old salary was $55,000, what is his new salary?

helppp

Answers

Answer:

we simply do - 55,000*105/100

Which is 55,000*1.05

And that is 57750

So his new salary is $57750

Thanks and mark me brainliest becuz i have good answer :)

Evaluate 3n + 4^2 when n = 2

Answers

Answer:

Step-by-step explanation:

3n + 4^2

n = 2

3(2) + 4^2 = 6 + 16 = 22

What is 0.3709 rounded to 2 decimal places?

Answers

Answer:

If its to the left the answer is 1 and if its to the right the answer is 10 i think

Step-by-step explanation:

sorry if its wrong

Write log7(2 ⋅ 6) + log73 as a single log. Log Subscript 7 Baseline 11 Log Subscript 7 Baseline 15 Log Subscript 7 Baseline 36

Answers

Answer:

C. log7 36....................................

The given logarithmic expressions together can be written as log₇ 36

What is a logarithmic function ?

The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function.

Formulae for logarithmic function are,

LogAB = LogA + LogB

Logₐaᵇ = b

Given that,

= log₇(2 x 6) + log₇3

= log₇ 36

We have the result

log A + log B = log AB

Here the question is log₇(2 x 6) + log₇3.

Using the property of logarithm we will get,

= log₇(2 x 6) + log₇3

= log₇(2 x 6 x 3)

= log₇ 36

So, log₇(2 x 6) + log₇3 = log₇ 36

To know more about Logarithmic function check:

https://brainly.com/question/27389970

#SPJ6

Can someone please help me and explain

Answers

(2x-3)+(6x+7)= 180
(2x•6x)+(-3+7)= 180
(12x)+(4) = 180
12x= 180-4
x= 176/12
x= 14.67

ratio 11 to 6 in perimeter

Answers

Answer: the answer will be 6/4

Step-by-step explanation:

Ques

The set of values (63, 64, 65, 66} represents solutions of which inequality?

Answers

Answer: 63 < N ≤ 66

Step-by-step explanation:

We have the set:

(66, 64, 65, 66]

First.

When we have an end with the signs "(" or ")" means that the element near the sign does not belong to the set, this would be an "open" end. Usually used for the symbols > and <

While the sign "[" or "]" (in some cases the symbols { and } are used instead)

means that the value next to it are included in the set. Usually used for the symbols ≤ and ≥.

Then in the set: (63, 64, 65, 66} the value 63 does not actually belong, and value 66 does belong.

Then this set is written as:

Answers

Answer:

Every linear equation that is a conditional equation has one solution. However, not every linear equation in one variable has a single solution. There are two other cases: no solution and the solution set of all real numbers. ... Therefore, the equation is always true.

Step-by-step explanation:

We want to see if a one-variable equation always has only one solution.

This is false, as one-variable equations can have no solutions or more than one solution.

So we start with the statement:

"A one-variable equation always has only one solution".

We need to find a counterexample to prove that this is false, and there are really easy counterexamples, like:

x^2 - 4 = 0

This is a one-variable equation, and solving it we have:

x^2 = 4

x = ± √4 = ±2

So here we have two solutions, 2 and -2, thus the statement is false.

If you want to learn more, you can read:

https://brainly.com/question/16797952

help please i’ll give extra points

Answers

one output for each imput

In ΔSTU, u = 40 inches, ∠S=73° and ∠T=71°. Find the length of t, to the nearest inch.

Answers

Answer: 64 inches

Step-by-step explanation: Solve using sohcahtoa for missing info

please help i dont know 7th grade math cry

Answers

Vertical angles are always equal, so you can set them equal to each other.

3x + 8 = 35

3x = 27

x = 9

Answer:

so.. this means that they're equal...

so.. 8 + x = 35

u need to solve for x...

so u do, 35 - 8 = 27

so it would be..

and 27 divide 3 = 9

so x = 9

so the equation would be...

(3 x 9 + 8) = 35

SO, the answer is 9

Step-by-step explanation:

can I have brainliest please? hee hee

can somebody please help kinda low on point so i would be greatful for real answers no fake!

Answers

Answer:

I think it would be the Thrid Option if its talking about a Can of Soup. Most cans Of soup are measured in Ounces for Whats contained inside.

i think it’s letter c

Other Questions

solve the initial value problem ( x 2 5 ) y ' 2 x y = 2 x ( x 2 5 ) with initial condition y ( 2 ) = 7 What is the missing step in solving the inequality 4(x 3) + 4 < 10 + 6x?1. The distributive property: 4x 12 + 4 < 10 + 6x2. Combine like terms: 4x 8 < 10 + 6x3. The addition property of inequality: 4x < 18 + 6x4. The subtraction property of inequality: 2x < 18 5. The division property of inequality: ________x < 9x > 9x < x is less than or equal to negative StartFraction 1 Over 9 EndFraction.x > x is greater than or equal to negative StartFraction 1 Over 9 EndFraction. if somone inhales forcfully what is the size of the thoracic cavity A C++ switch allow more than one case to be executed. O True O False which of the following accurately describes the process of factor analysis in the identification of personality traits? group of answer choices A stock has a beta of 1.88, the market risk premium is 7.3%, and the risk-free rate is 3.25 percent. What must the expected return on this stock be? A. 16.97% B. 16.44% C. 15.92% D. 17.45% E. 15.41% I NEEDD HELPPP PLEASEEEE a nurse is caring for a client who is being admitted for an acute exacerbation of ulcerative colitis. which of the following actions should the nurse take first? Toy wagons are made to sell at a craft fair. It takes 4 hours to make a small wagon and 6 hours to make a large wagon. The owner of the craft booth will make a profit of $12 for a small wagon and $20 for a large wagon and has no more than 60 hours available to make wagons. The owner wants to have at least 6 small wagons to sell statistics that allow for inferences to be made about a population from the study of a sample are known as____ bobbie s problems at school have been identified as rooted in family pathology. the most likely recommendation will be for family therapy. True or false ? at the dawn of industrialization, why were entrepreneurs important to changing economies in europe? check all that apply. on weekdays customers arrive at a hotdog street vendor at the rate of 3 per 10 minute interval. what is the probability that exactly 10 customers will arrive at the vendor for the next 30 minute. Soccer A soccer team estimates that they will score on 8% of the cornerkicks. In next week's game, the team hopes to kick 15 corner kicks. What arethe chances that they will score on 2 of those opportunities?Soccer again if this team has 200 corner kicks over the season, what are the chances that they score more than 22 times? Downtown Bank provides lockbox services. They estimate that you can reduce your average mail time by 1. 6 days and your combined clearing and processing time by. 5 days by implementing their system. Your firm receives 654 checks a day with an average value of $975 each. The current T-Bill rate is. 009 percent per day. Assume a 365-day year. The bank will charge your firm $. 17 per check. What is the net present value from installing this system? A thin layer of oil (n = 1.25) is on top of a puddle of water (n = 1.33). If normally incident 500-nm light is strongly reflected, what is the minimum nonzero thickness of the oil layer in nanometers?A. 600B. 400C. 200D. 100 A and B are two events. Let P(A) = 0.65, P (B) = 0.17, P(A|B) = 0.65 and P(B|4) = 0.17 Which statement is true?1. A and B are not independent because P(A|B) + P(A) and P(B|4) + P(B).2. A and B are not independent because P (A|B) + P(B) and P(B|4) + P(A)3. A and B are independent because P (A|B) = P(A) and P(BIA) = P(B).4. A and B are independent because P (A|B) = P(B) and P(B|A) = P(A). Determine the properties of the binary relation R on the set { 1, 2, 3, 4, } where the pair (a, b) is in R if a |b. Circle the properties:Is this relation Reflective?Is this relation Symmetric?Is this relation Antisymmetric?Is this relation Transitive? you purchase one microsoft december $140 put contract for a premium of $5.30. what is your maximum possible profit? assume each contract is for 100 shares. Compare the different ways in which the Belgium Sri Lanka have death with the problem of cultural diversity