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

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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

attachment?

step-by-step explanation:

Answer from: Quest

answer: the answer is ann

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