Find a point on the y-axis that is equidistant from (-5,2) and (9,-2).

A point on the y-axis is always represented as (0, y).

Answer: The point on the y-axis that is equidistant from (- 5, 2) and (9, -2) is (0, -7).

Let us proceed step by step.

Explanation:

Let us consider the point on the y-axis to be (0, y) as the x-coordinate is 0 on the y-axis.

So,the point (0, y) is equidistant from (- 5, 2) and (9, -2).

Since their distance is equal we can apply the distance formula.

Applying distance formula,

d = √[(x₂ − x₁)²+(y₂ − y₁)²]

= √[{0 - (- 5)}² + (y - 2)²] = √[(9 - 0)² + ( -2 - y)²]

Now simplifying step by step to find the value of y.

25 + y² + 4 - 4y = 81 + 4 + y² + 4y

29 - 4y = 85 + 4y

8y = -56

y = -56 / 8 = -7

The value of y is -7.

Hence, the point on the y-axis that is equidistant from (- 5, 2) and (9, -2) is (0,-7).