Question

Two vertices of a triangle are (3, -1) and (- 2. 3). Orthocentre of triangle lies at the origin. Find the coordinates of third vertex.

Answer 1

Vertices of ∆ABC are A(h, k), 5(3, – 1) and (- 2,3).

vertex A is intersecting point of AB and AC. 

Side AB passes through point (3, – 1) and is perpendicular to DC whose slope is – 3/2

Similarly AC passes through (- 2,3) and is perpendicular to OB, whose slope is – 1/3. 

Thus equation of side AC

y – 3 = 3(x + 2)

⇒ 3x – y + 9 = 0 …(ii)

Solving equation (i) and (ii)

x = – 36/7 and y = – 45/7

Thus, coordinates of A is ( – 36/7, – 45/7)