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

Evaluate 3n + 4^2 when n = 2

Answers

Answer:

22

Step-by-step explanation:

3n + 4^2

n = 2

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

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

An employee earned $10.00 per hour and then received a raise that paid
him $12.50 per hour. What is the percent change in the amount of money
he makes per hour. ?

Answers

Answer:

25% pay raise

Step-by-step explanation:

12.50-10.00=2.50

2.50/10.00=1/4

1/4=25%

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:

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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

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

Help!!! 30 Points!!!

Answers

Answer:

45,90,135,180,225,270,315,360

Step-by-step explanation:

Answer:

45,90,135,180,225,270,315,360

Step-by-step explanation:

Hope this helps :)

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)

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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! :)

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

ratio 11 to 6 in perimeter

Answers

Answer: the answer will be 6/4

Step-by-step explanation:

Cole learned that newly-minted
coins are put into bags. The
mint puts 2,000 half-dollar
coins into 1 bag. What is the
value of 11 bags?

Answers

Answer:

11000 dollars.

Step-by-step explanation:

Interesting question.

1 bag has 2000 half dollars in it.

2000 half dollar coins have a value of 2000 * 1/2 = 1000 dollars.

11 bags = 1000 * 11 = 11000 dolars.

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

Which statement(s) describe parallel lines? Choose ALL that apply.


A. Parallel lines never cross or meet.

B. Parallel lines create a 90 degree angle.

C. Parallel lines intersect.

Answers

Parallel lines never cross or meet

Definetily its A) Parallel linea never cross or meet.

Is 4x+1=f(x) a quadratic function?

Answers

Answer: no

Step-by-step explanation:

the x has to be squared to form a parabola with a vertex and 2 x intercepts

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:

63 < N ≤ 66

Such that N is an integer number.

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  

(

x

A

,

y

A

)

= (2, 5)

Point B  

(

x

B

,

y

B

)

= (2, -2)

Objective :

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

Formula :

Slope

 

m

=

y

B

y

A

x

B

x

A

Solution:

Slope

 

m

=

2

5

2

2

=

7

0

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.

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

please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

The solution is -3.

The graph is attached.

Step-by-step explanation:

To solve, first subtract 2 from both sides to get [tex]5q\geq -15[/tex]. Now divide 5 from both sides to get [tex]q\geq -3[/tex].

The graph representing this is attached.

Hope it helps and is correct!

will a one variable equation always have only one solution

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

Explain why the net shown here cannot be the net of a cube

Answers

Answer:

there is an extra square missing

Step-by-step explanation:

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

Now practice solving some problems.


Find the solution of y = –3x – 1 for x = –5.


A.
(–5, –16)


B.
(–16, –5)


C.
(–5, 14)


D.
(14, –5)

Answers

Answer:

The answer is C. (-5, 14)

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)

PLZZZZZZZZZZZZ HELPpppppp

Answers

Answer:

2x2-y=1

4-y=1

-y=1-4

-y=-3

y=3

Step-by-step explanation:

Evan is going to invest in an account paying an interest rate of 6.1% compounded
continuously. How much would Evan need to invest, to the nearest ten dollars, for
the value of the account to reach $7,800 in 14 years?

Answers

Answer:3320

Step-by-step explanation:

18/20 + 12/20 (simpfiy it )

Answers

Answer:

1 [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Add the numerators and keep the same denominator.

18/20 + 12/20 = 30/20

30/20 = 1 [tex]\frac{1}{2}[/tex]

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

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 :)

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