Question

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

• A. (5, 2)
• B. (4, 4)
• C. (-2, 1)
• D. (2, 3)

Answer 1

The correct option is B (4, 4)

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

Slope of PQ = $\frac{-1}{slopeoftheline}$

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

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

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

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

2h + k = 12 -(1)

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