Question

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)

Answer 1

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

$P''(-1, -2),\quad Q''(0, 3),\quad R''(1, 0)$

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.