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victus00 [196]
2 years ago
9

Given directed line segment PR, find the coordinates of Q on PR such that the ratio of PQ to QR is 2:1.

Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
4 0

Answer:

4/3, -3

Step-by-step explanation:

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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 t
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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″.

<u>Case I :</u>  ΔPQR dilated to ΔP'Q'R'

The co-ordinates of P' and Q' are given by

P'(3\times 1.5, -4\times 1.5)=P'(4.5, -6),\\\\Q'(5\times 1.5, -1\times 1.5)=Q'(7.5, -1.5).

<u>Case II :</u>  ΔP'Q'R' dilated to ΔP''Q''R''

The co-ordinates of P'' and Q'' are given by

P''(4.5\times 2, -6\times 2)=P'(9, -12),\\\\Q'(7.5\times 2, -1.5\times 2)=Q'(15, -3).

Thus, the co-ordinates of the vertices P'' and Q'' are (9, -12) and (15, -3).

Option (D) is CORRECT.

<u></u>

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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