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

its a little blurry tbh

step-by-step explanation:

Ineed y’all to me with 13-20 so i can get this done early

Answer from: Quest

answer: 2/4

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:00, MengXiong1

Tamera puts 15/4 gallons of gasoline in her car. which mixed number represents the gallons of gasoline? a) 2 3/4 gallons b) 3 1/4 gallons c) 3 3/4 gallons d) 4 1/2 gallons answer it's worth a lot of points!

Answers: 3

continue

Mathematics, 21.06.2019 18:30, jorozco3209

Haruka hiked several kilometers in the morning. she hiked only 66 kilometers in the afternoon, which was 25% less than she had hiked in the morning. how many kilometers did haruka hike in all?

Answers: 1

continue

Mathematics, 21.06.2019 22:00, rhineharttori

Here is my question! jayne is studying urban planning and finds that her town is decreasing in population by 3% each year. the population of her town is changing by a constant rate. true or false?

Answers: 2

continue

Mathematics, 21.06.2019 23:00, kealalac1

Afunction, f(x), represents the height of a plant x months after being planted. students measure and record the height on a monthly basis. select the appropriate domain for this situation. a. the set of all positive real numbers b. the set of all integers oc. the set of all positive integers od. the set of all real numbers reset next

Answers: 3

continue

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...