MATH SOLVE

4 months ago

Q:
# 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″?P″(4.5, -6) and Q″(7.5, 1.5)P″(4.5, -6) and Q″(7.5, -1.5)P″(-9, 12) and Q″(15, -3)P″(9, -12) and Q″(15, -3)P"(-9, -12) and Q"(-15, -3)

Accepted Solution

A:

Answer: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.Step-by-step explanation: