Mathematics, 07.11.2019 17:31 dan7478

Triangle pqr is transformed to triangle p'q'r'. triangle pqr has vertices p(8,0),
q(6,2), and r(-2,-4). triangle p'q'r' has vertices p'(4,0), q'(3, 1), and r'(-1,
-2).

plot triangles pqr and p'q'r' on your own coordinate grid.

part a: what is the scale factor of the dilation that transforms triangle pqr to
triangle p'q'r'? explain your answer. (4 points)

part b: write the coordinates of triangle p'q''r" obtained after p'q'r' is
reflected about the y-axis. (4 points)

part c: are the two triangles pqr and p'q''r''congruent? explain your answer.
(2 points)

Answers: 1

Show answers

Answers

Answer from: Amyra2003

Part A) The scale factor is 0.5. The draw in the attached figure

Part B) The coordinates of triangle P''Q''R" are P''(-4,0),Q''(-3, 1) and R''(1,

-2)

Part C) Triangles PQR and P''Q''R are similar but not congruent

Step-by-step explanation:

Part A) Plot triangles PQR and P'Q'R' on your own coordinate grid.

What is the scale factor of the dilation that transforms triangle PQR to

triangle P'Q'R'?

we have

Triangle PQR has vertices P(8,0),

Q(6,2), and R(-2,-4)

Triangle P'Q'R' has vertices P'(4,0), Q'(3, 1), and R'(-1,

-2)

using a graphing tool

Plot triangles

see the attached figure

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

Let

z ----> the scale factor

$z=\frac{P'Q'}{PQ}=\frac{Q'S'}{QS}=\frac{R'P'}{RP}$

Find the measure of length side P'Q' and PQ

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the measure of length side P'Q'

P'(4,0), Q'(3, 1)

substitute the values in the formula

$d_P'_Q'=\sqrt{(1-0)^{2}+(3-4)^{2}}$

$d_P'_Q'=\sqrt{(1)^{2}+(-1)^{2}}$

$d_P'_Q'=\sqrt{2}\ units$

Find the measure of length side PQ

P(8,0),

Q(6,2)

substitute the values in the formula

$d_P_Q=\sqrt{(2-0)^{2}+(6-8)^{2}}$

$d_P_Q=\sqrt{(2)^{2}+(-2)^{2}}$

$d_P_Q=\sqrt{8}\ units$

Find the scale factor

$z=\frac{P'Q'}{PQ}$

substitute the values

$z=\frac{\sqrt{2}}{\sqrt{8}}=0.5$

Part B) Write the coordinates of triangle P''Q''R" obtained after P'Q'R' is

reflected about the y-axis

we know that

The rule of a reflection of a point across the y-axis is equal to

(x,y) -----> (-x,y)

we have

Triangle P'Q'R' has vertices P'(4,0), Q'(3, 1), and R'(-1,

-2)

Applying the rule of reflection across the y-axis

P'(4,0) -----> P''(-4,0)

Q'(3, 1) -----> Q''(-3, 1)

R'(-1,

-2) ----> R''(1,

-2)

therefore

The coordinates of triangle P''Q''R" are P''(-4,0),Q''(-3, 1) and R''(1,

-2)

Part C) Are the two triangles PQR and P'Q''R''congruent?

we know that

If two triangles are congruent, then their corresponding sides and its corresponding angles are congruent

In this problem, the corresponding angles between triangle PQR and P''Q''R'' are congruent but the corresponding sides are not congruent.

The length sides of triangle P''Q''R'' is one half of the length sides of triangle PQR

therefore

Triangles PQR and P''Q''R are similar but not congruent

Triangle pqr is transformed to triangle p'q'r'. triangle pqr has vertices p(8,0), q(6,2), and r(-2,-

Answer from: Quest

it is b)

hope this : )

step-by-step explanation:

Answer from: Quest

answer: you need to organize this better it does not make sense.

step-by-step explanation: ?

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Write the fraction or mixed number and the decimal shown by the model

Answers: 2

Answer

Mathematics, 21.06.2019 20:10

Look at the hyperbola graphed below. the hyperbola gets very close to the red lines on the graph, but it never touches them. which term describes each of the red lines? o o o o a. asymptote b. directrix c. focus d. axis

Answers: 3

Answer

Mathematics, 21.06.2019 22:00

Given sin∅ = 1/3 and 0 < ∅ < π/2 ; find tan2∅ a. (4√2)/9 b. 9/7 c. (4√2)/7 d.7/9

Answers: 2

Answer

Mathematics, 22.06.2019 01:30

What is the solution for the following system of equations? use any method to solve. 2x + 8y = 4 x = -3y + 5 question 4 options: x = 14, y= -3 x = 2, y = -3 x = -3, y = -3 x = 12, y = 5

Answers: 1

Answer

You know the right answer?

Triangle pqr is transformed to triangle p'q'r'. triangle pqr has vertices p(8,0),
q(6,2), and...

Questions

Mathematics, 11.06.2021 15:50

Is 25/4 grater then 40/8 ...