Question

A circle has a diameter that extends from (4.-6) to (-8,10). What are the coordinates the center of the circle?​

Answer 1

Answer: (-2, 2)

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Reason:

For now we'll only focus on the x coordinates. They are 4 and -8. Plot them on a number line and find the midpoint. To do this, add those values up and divide by two

(4 + (-8))/2 = -4/2 = -2

The value -2 is right in the middle of 4 and -8; hence it's the midpoint.

Repeat those steps for the y coordinates

(-6+10)/2 = 4/2 = 2

These two midpoints help lead to (x,y) = (-2, 2) which is the midpoint the given endpoints. By extension, it is the center of the circle.

Visual confirmation is shown below. I used the midpoint command in GeoGebra. Desmos is another graphing tool you can use.