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)

 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.

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