Question

Orthocentre of the triangle formed by the lines $x + y = 1$and $xy = 0$is.

• A. (0,0)
• B. (0,1)
• C. (1,0)
• D. (–1,1)

Answer 1

Answer: (A)

(0,0)

Answer 2

Given lines are $x + y = 1$ and $x y = 0$

when $x = 0$ , then $y = 1$

when $x = 1$ , then $y = 0$

$\therefore$ (0, 1) and (1, 0) are the vertices of triangle. Clearly, triangle is right-angled isosceles. Orthocentre of right-angled triangle is same as the vertex of right angle.

Therefore point of intersection of $x + y = 1$ and $x y = 0$is (0, 0).