Triangle pqr is transformed to triangle p′q′r′. triangle pqr has vertices p(4, −8), q(0, 12), and r(−4, 0). triangle p′q′r′ has vertices p′(1, −2), q′(0, 3), and r′(−1, 0).

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)

Part A:

The scale factor is 1/4, because you obtain the coordinates of points P', Q', R' by dividing the coordinates of P, Q and R respectively by 4.

Part B:

Reflecting about the y axis causes a sign swap in the x coordinate. So, the new point will be

Part C:

The triangles are similar, but not congruent. When you transform PQR into P'Q'R', you get a scaled version of the original triangle. This means that the angles and the proportion between sizes will be the same, but the length are scaled by 1/4, and the area is consequentially scaled by 1/16.

Triangles P'Q'R' and P''Q''R'' are congruent, so they are both similar but not congruent to the original triangle.

the answer to the question is a  

it has the same slope and the same y-intercept.

y = x + 95

y = 42 + 95

y=137 mm hg