Question

select the correct answer. triangle pqr is dilated by a scale factor of 1.5 to form triangle pqr. this triangle is then dilated by a scale factor of 2 to form triangle pqr. 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)

Explanation:

Step1: Calculate the combined scale factor

The combined scale factor is \(1.5\times2 = 3\).

Step2: Find the coordinates of \(P''\)

For point \(P(3,-4)\), multiply each coordinate by the scale factor \(3\).
\(x\)-coordinate: \(3\times3=9\)
\(y\)-coordinate: \(-4\times3=-12\)
So \(P''=(9, - 12)\)

Step3: Find the coordinates of \(Q''\)

For point \(Q(5,-1)\), multiply each coordinate by the scale factor \(3\).
\(x\)-coordinate: \(5\times3 = 15\)
\(y\)-coordinate: \(-1\times3=-3\)
So \(Q''=(15,-3)\)

Answer:

D. \(P''(9, - 12)\) and \(Q''(15, - 3)\)