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The Mid-Point Theorem

In the adjoin...

Question

In the adjoining figure given below $S T ∥ Q R$ , then what is the value of y?

A

5

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B

9

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C

12

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D

15

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Solution

The correct option is B 9
$S i n c e, S T ∥ Q R \Rightarrow \frac{P S}{S Q} = \frac{P T}{T R}$ $(by mid-point theorem)$
$\Rightarrow \frac{P S}{S Q} + 1 = \frac{P T}{T R} + 1$
$\Rightarrow \frac{P S + S Q}{S Q} = \frac{P T + T R}{T R}$ or $\Rightarrow \frac{P Q}{S Q} = \frac{P R}{T R}$
$\Rightarrow \frac{2 y}{y - 3} = \frac{2 y + 3}{y - 2}$
$\Rightarrow 2 y^{2} - 4 y = 2 y^{2} - 6 y + 3 y - 9$
$\Rightarrow - 4 y = - 3 y - 9$
$\Rightarrow y = 9$

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