Question

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.

Part B: Write the coordinates of triangle P′′Q′′R′′ obtained after P′Q′R′ is reflected about the y-axis.

Part C: Are the two triangles PQR and P′'Q′'R′' congruent? Explain your answer.

Answer 1

Answer:

Part A: Triangle P' Q' R' is half the size of the original triangle. The scale factor is probably 1/3.

Triangle P' Q' R' is half the size of the original triangle. The scale factor is probably 1/3.Part B: P'(1, −2), Q'(0, 3), and R'(−1, 0).

Triangle P' Q' R' is half the size of the original triangle. The scale factor is probably 1/3.Part B: P'(1, −2), Q'(0, 3), and R'(−1, 0).Part C: No, the triangles are not congruent. If the second triangle didn't have a dilation, and instead have a reflection of the first triangle, then it would be congruent.