Question

The foot of the perpendicular of (3, 6) on the line $x-2y+4=0$ is

• A. (4,4)
• B. (2,3)
• C. (5,2)

Answer 1

The correct option is A (4,4)

Let the co-ordinates of Q (foot of the perpendicular) be (h,k)

Slope of PQ = $\frac{-1}{\text{slope of the line}}$

= $\frac{\frac{-1}{1}}{2}=-2$

We can find the slope using P(3,6) and Q(h,k)

$\Rightarrow \frac{k-6}{h-3}=-2$

$\Rightarrow k-6=-2h+6$

$2h+k=12...\left(i\right)$

(h,k) is a point on $x-2y+4=0$

Hence, $h-2k+4=0...\left(ii\right)$

On solving (1) and (2), we get h = 4 and k = 4.

Thus, the foot of the perpendicular of (3, 6) on the line $x-2y+4=0$ is (4,4)