Triangle pqr is transformed to triangle p′q′r′. triangle pqr has vertices p(3, −6), q(0, 9), and r(−3, 0). triangle p′q′r′ has vertices p′(1, −2), q′(0, 3), and r′(−1, 0). 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)

QUESTION 1

Triangles PQR and P'Q'R' has been plotted in the graph.

The green triangle is triangle PQR.

The red triangle is triangle P'Q'R'.

See attachment for graph.

QUESTION 2

Part A

The scale factor can be calculated using the formula,

QUESTION 3

Part B

For a reflection in the y-axis, we negate the x-coordinates. So we negate the x-coordinates of P'Q'R' to obtain the coordinates of P"Q"R".

This implies that,

QUESTION 4

Part C

The two triangles PQR and P′'Q′'R′' are not congruent. The reason is that the two triangles are not equal in all respect. The side lengths are not the same.

If two triangles are congruent, they will have exactly the same three sides and the same three angles.

This means that the two triangles must have the same size and shape. But  triangles PQR and P′'Q′'R′'  do not have the same size therefore they are not congruent.

See graph

option: d is correct

step-by-step explanation:

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2