Question

The coordinates of the orthocenter of the triangle, having vertices (0, 0), (2, –1) and (–1, 3), are

• A. (4, –3)
• B. (–4, 3)
• C. (4, 3)
• D. (–4, –3)

Answer 1

The correct option is D

(–4, –3)

Let A ≡ (0, 0), B ≡ (2, –1) and (–1, 3). Since AL $\perp$ BC, therefore

Equation of AL is

$y-0=-\frac{2+1}{-1-3}(x-0)(\because slopeofBC=\frac{-1-3}{2+1})\Rightarrow 3x+4y=0\cdots \left(1\right)$

Since BM $\perp$ AC, therefore equation of BM is

$y+1=-\frac{0+1}{0-3}(x-2)(\because slopeofAC=\frac{0-3}{0+1})$

$\Rightarrow$ x – 3y = 5 …… (2)

Solving equations (1) and (2), we get

x = –4, y = –3.

Thus, the coordinates of the orthocenter are

H(–4, –3)