Question

The coordinates of vertices of base BC of an isosceles triangle ABC are given by B(1, 3) and C(–2, 7) which of the following points can be the possible coordinates of the vertex A?

Options

• `(-7, 1/8)`

• (1, 6)

• `(-1/2, 5)`

• `(-5/6, 6)`

Answer 1

`bb((-5/6, 6)`

Explanation:

Since AB = AC 

 ⇒ AB² = AC²

(x – 1)² + (y – 3)² = (x + 2)² + (y – 7)²

⇒ x² – 2x + 1 + y² – 6y + 9 

= x² + 4x + 4 + y² – 14y + 49

⇒ – 6x – 8y + 43 = 0

⇒ 6x – 8y + 43 = 0                  ...(i)

Only `(-5/6, 6)` satisfies the equation (i).