Question

A circle has a diameter with endpoints of (-1, 5) and (5, 3). What is the center of the circle?

(2, 4)
(4, 4)
(2, 5)
(5, 1)

Answer 1

(2, 4)

Explanation:

The center is the midpoint of the diameter.

(x, y) = ((-1 + 5)/2, (5 + 3)/2)

(x, y) = (2, 4)

Answer 2

The center is (2,4)

EXPLANATION

The given circle has a diameter with endpoints of (-1, 5) and (5, 3).

We use the midpoint formula to find the center of the circle

`( (x_1+x_2)/(2) ,(y_1+y_2)/(2))`

We plug in the points to obtain;

`( ( - 1+5)/(2) ,(5+3)/(2))`

This simplifies to ;

`( ( 4)/(2) ,(8)/(2))`

`( 2 ,4)`