Question

The point on the line 4x − y – 2 = 0 which is equidistant from the point (−5, 6) and (3, 2) is ______.

Options

• (2, 6)

• (4, 14)

• (1, 2)

• (3, 10)

Answer 1

The point on the line 4x − y – 2 = 0 which is equidistant from the point (−5, 6) and (3, 2) is (4, 14).

Explanation:

Let the point be P(a, b) which lies on line 4x − y – 2 = 0   ...(i)

and point P is equidistant from A(−5, 6) and B(3, 2).

Then, PA = PB or PA² = PB²

= (a + 5)² + (b − 6)² = (a − 3)² + (b − 2)²

= a² + 10a + 25 + b² – 12b + 36

= a2 − 6a + 9 + b² − 4b + 4

= 16a − 8b + 48 = 0

= 2a − b + 6 = 0   ...(ii)

On solving equations (i) and (ii), we get a = 4, b = 14