Question

The equations of the perpendicular bisectors of the sides AB and AC of a triangle ABC are x - y + 5 = 0 and x + 2y = 0, respectively. If the point A is (1, - 2), find the equation of the line BC.

Answer 1

Let the coordinates of B and C be (x₁, y₁) and (x₂, y₂) respectively. Let m₁ and m₂ be the slopes of AB and AC respectively. Then,

Let F and E be the mid point of AB and AC respectively, Then, the coordinates of E and F are

On solving Eqs. (iii) and (iv), we get