Find the point on the y-axis

Question

which is equidistant from (-3,-6) and (3,4). The segment joining F(-6,11) and G(3,4) is divided into four equal?

Answer 1

Let the point be P(0, a).           [Since, the point is on the y - axis, its x - coordinate must be 0]

Let the points are A(- 3, - 6) and B(3, 4).

From the given data AP = BP.

√[(- 3 - 0)² + (-  6 - a)²] = √[(3 - 0)² + (4 - a)²]

√[(- 3)² + (-  6 - a)²] = √[(3)² + (4 - a)²]

Squaring on both sides.

(- 3)² + (-  6 - a)² = (3)² + (4 - a)²

9 + (-  6 - a)² = 9 + (4 - a)²

(-  6 - a)² = (4 - a)²

a + 6 = ±(a - 4)

a + 6 = a - 4  and  a + 6 = - a + 4

6 = - 4  and  2a = 4 - 6 = - 2

6 = - 4, is impossible.

So, a = - 2/2 = - 1.

Therefore, the point on the y - axis is (0, - 1).