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 $\Delta$ OPQ is

• A. 48
• B. 16
• C. 32
• D. None of these

Answer 1

The correct option is A 48

$LetOR\perp PQThen,OR=\frac{|4\left(0\right)+3\left(0\right)+30|}{\sqrt{16+9}}=\frac{30}{5}=6$

$\therefore PR=\sqrt{O{P}^2-O{R}^2}=\sqrt{100-36}andPQ=2PR=16.\therefore Areaof△OPQ=\frac{1}{2}\times PQ\times QR=\frac{1}{2}\times 16\times 6=48$