Question

coordinate plane with triangles LMN and PQR with L at negative 3 comma 2, M at 1 comma 6, N at 1 comma 2, P at negative 2 comma 3, Q at 0 comma 5, and R at 0 comma 3

Which set of transformations would prove ΔLMN ~ ΔPQR?

Answer 1

Dilation with center (-1, 4) and scale factor 1/2.

Check: c = 2P - L = 2(-2,3) - (-3,2) = (-1,4). With center c and s = 1/2,
c + 1/2(L - c) = (-2,3) = P,
c + 1/2(M - c) = (0,5) = Q,
c + 1/2(N - c) = (0,3) = R.

So ΔLMN dilates by 1/2 about (-1,4) to ΔPQR, proving similarity.