Question

Triangle PQR is dilated by a scale factor of 1.5 to form triangle P′Q′R′. This triangle is then dilated by a scale factor of 2 to form triangle P″Q″R″. If vertex P is at (3, -4) and vertex Q is at (5, -1), what are the coordinates of vertices P″ and Q″?
A. P″(4.5, -6) and Q″(7.5, 1.5)

B. P″(4.5, -6) and Q″(7.5, -1.5)

C. P″(-9, 12) and Q″(15, -3)

D. P″(9, -12) and Q″(15, -3)

E. P"(-9, -12) and Q"(-15, -3)

Answer 1

Answer:  The correct option is (D) P″(9, -12) and Q″(15, -3).

Step-by-step explanation:  Given that triangle PQR is dilated by a scale factor of 1.5 to form triangle P′Q′R′. This triangle is then dilated by a scale factor of 2 to form triangle P″Q″R″.

The co-ordinates of vertices P and Q are (3, -4) and (5, -1) respectively.

We are to find the co-ordinates of the vertices P″ and Q″.

Case I :  ΔPQR dilated to ΔP'Q'R'

The co-ordinates of P' and Q' are given by

Case II :  ΔP'Q'R' dilated to ΔP''Q''R''

The co-ordinates of P'' and Q'' are given by

Thus, the co-ordinates of the vertices P'' and Q'' are (9, -12) and (15, -3).

Option (D) is CORRECT.

Answer 2

If you want to make it easier, just skip it and dilate by 3 instead of by 1.5 and then by 2. The only reason I can instantly assume it's D, it's because on vertex P, (3, -4) is (9,-12), the only answer with +9.