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Select the correct answer. 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).

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Answer:

  D. P″(9, -12) and Q″(15, -3)

Step-by-step explanation:

Each dilation multiplies the coordinate values by the scale factor. The double dilation multiplies each coordinate by the product of the dilation factors:

  1.5 × 2 = 3

Then ...

  P" = 3P = 3(3, -4) = P"(9, -12)

  Q" = 3Q = 3(5, -1) = Q"(15, -3)

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