Question

Two vertices of a triangle are (5, –1) and (–2, 3). If orthocentre of the triangle is the origin then coordinates of third vertex, are

• A. (–4, –7)
• B. (–4, 7)
• C. (4, 7)
• D. (4, –7)

Answer 1

Answer: (A)

(–4, –7)

Answer 2

Slope of BC = –$\frac{4}{7}$;Slope of AD =$\frac{q}{p}$; m₁m₂ = –1

$\left( \frac { - 4 } { 7 } \right)$ $\frac{q}{p}$=–1Ž7p= 4q … (1)

slope of CA = $\frac{3}{p + 2}$

slope of BE

= slope of BO = –$\frac{1}{5}$

But m₁m₂ = –1; $\left( - \frac{1}{5} \right)$= –1

Ž 5p – q + 13 = 0 …(2)

solving (1) and (2), we get p = –4, q = –7