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).

Question

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)

oobleck · Accepted Answer

A: Use the distance formula to find lengths PQ and P'Q'
The scale factor is P'Q' / PQ

B: (x,y) → (-x,y)

C: Unless the scale factor from (A) is 1, the two are not congruent, since reflection does not change any side lengths.

oobleck · Answer

oops. For (A), you need to check all three sides. to be sure the ratios are all the same. It might be easier just to make sure that the coordinates have a common ratio.