Question : M is the mid-point of side QR of a parallelogram PQRS (P being on the top left hand, followed by other points going clockwise). The line SM is drawn intersecting PQ produced at I. What is the length (in terms of the length of SR) of PI?
Option 1: $\frac{3 \mathrm{SR}}{2}$
Option 2: $\frac{\mathrm{SR}}{2}$
Option 3: $2 \mathrm{SR}$
Option 4: $\mathrm{SR}$
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Correct Answer: $2 \mathrm{SR}$
Solution :
In $\triangle$PIS, M is the midpoint of QR and QM || PS
$\therefore$ Q is the midpoint of PI [converse of mid-point theorem]
⇒ PI = 2PQ
Given, PQRS is a parallelogram.
Since, in parallelogram opposite sides are parallel and equal.
Therefore, PQ = SR
⇒ PI = 2SR
Hence, the correct answer is $2 \mathrm{SR}$.
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