First slide

Equation of line in Straight lines

Question

If P and Q are two points on the line 4x + 3y + 30 = 0 such that OP = OQ = 10, where O is the origin, then the area of the $∆$ OPQ is

Moderate

A

48
B

16
C

32
D

none of these

Solution

Let OR $⊥$ PQ
Then, $O R = \frac{|4 (0) + 3 (0) + 30|}{\sqrt{16 + 9}} = \frac{30}{5} = 6$
$∴ P R = \sqrt{O P^{2} - O R^{2}} = \sqrt{100 - 36}$ and PQ = 2PR = 16
$∴ A r e a o f ∆ O P Q = \frac{1}{2} \times P Q \times O R$
$= \frac{1}{2} \times 16 \times 6 = 48$

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