Question

How to find the point that is equidistant from (5,-5) and (1,1)

Answer 1

Answer: (3, -2)

Explanation:

Your teacher wants you to find the midpoint. This is the point that is in the middle of the two given points. Let's call this M. So the distance from M to (5,-5) will be the same as the distance from M to (1,1)

The x coordinates of (5,-5) and (1,1) are 5 and 1 respectively.

Add them up: 5+1 = 6

Divide by two: 6/2 = 3

The x coordinate of the midpoint is x = 3

Repeat for the y values -5 and 1

Add: -5+1 = -4

Divide in half: -4/2 = -2

The y coordinate of the midpoint is y = -2

So the midpoint is M = (x,y) = (3,-2)

If you were to use the distance formula, you would find that

distance from (5,-5) to (3,-2) = distance from (3,-2) to (1,1)

This is what it means to be "equidistant" (aka "equally distant")