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

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)

jhonyy9 · Answer

like a first step i think may be more usefully understandably  than you draw a coordinate plane with these triangles

Mercury · Answer

part A: to find the scale factor from PQR to P'Q'R', calculate any side length on P'Q'R' and divide it by the corresponding side on PQR

example: you could pick side P'Q', which corresponds to PQ, and divide length of P'Q' / PQ

part B: to reflect P'Q'R' across the y-axis, multiply every x-cordinate in P'Q'R' by -1 to get the coordinates of P"Q"R"

part C: to determine congruency, you *could* calculate the side lengths of PQR and P"Q"R", or you could also think about what the steps were to get from PQR --> P'Q'R' ---> P"Q"R" and determine whether these transformations were rigid or not.