Find a point on the y-axis which is equidistant from the point (5,2) and (-4,3)

Question

I am getting confused in this problem. 

Answer 1

Use the distance formula.

The point on the y-axis is (0, y)

(d_(5,2)) = (5 - 0)² + (2 - y)²

(d_(-4,3)) = (-4 - 0)² + (3 - y)²

 

The two distances must be equal (the same)

 

(5 - 0)² + (2 - y)² = (-4 - 0)² + (3 - y)²

 

Can you solve for y and answer?

 

 

Answer 2

A point on the y-axis can be written as (0,y).

 

So, we want to choose y so that the distance from (0,y) to (5,2) is the same as the distance from (0,y) to (-4,3).

 

Using the distance formula, we have:

 

  √[(y-2)² + (0-5)²] = √[y-3)² + (0+4)²]

 

Squaring both sides and simplifying yields y² - 4y + 29 = y² - 6y + 25

 

                                                                            2y = -4

 

                                                                               y = -2

 

The point is (0, -2).