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″?

Answer 1

The coordinates of vertices P" and Q" after successive dilations by factors of 1.5 and 2 are (9, -12) and (15, -3), respectively.

Step-by-step explanation:

To find the coordinates of vertices P" and Q" after the dilations, we will apply the scale factors step by step to the original coordinates of vertices P and Q. Since triangle PQR is first dilated by a scale factor of 1.5 to form triangle P'Q'R', we will multiply the original coordinates by 1.5.

• The coordinates of P' will be (3 × 1.5, -4 × 1.5) = (4.5, -6).
• The coordinates of Q' will be (5 × 1.5, -1 × 1.5) = (7.5, -1.5).

Next, triangle P'Q'R' is further dilated by a scale factor of 2 to form triangle P"Q"R". We will multiply the coordinates of P' and Q' by 2.

• The coordinates of P" will be (4.5 × 2, -6 × 2) = (9, -12).
• The coordinates of Q" will be (7.5 × 2, -1.5 × 2) = (15, -3).

Therefore, the coordinates of vertices P" and Q" are (9, -12) and (15, -3), respectively.

Answer 2

The coordinates of vertex P″ are (9, -12) and the coordinates of vertex Q″ are (15, -3).

Step-by-step explanation: