Question

A circle has diameter endpoints of A(5, 10) and B(-3,4).

What are the coordinates of the center of the circle?
0 (4, -2)
o(-11, -2)
O (13, 16)
o (1,7)

Answer 1

(1,7)

Explanation:

Hi there!

The center of the circle is located in the middle two diameter endpoints. To find the coordinates of the center of the circle, calculate the midpoint of the two endpoints A and B.

Midpoint:
`((x_1+x_2)/(2) ,(y_1+y_2)/(2) )` where the two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points A(5, 10) and B(-3,4):

`((5+(-3))/(2) ,(10+4)/(2) )\\((5-3)/(2) ,(10+4)/(2) )\\((2)/(2) ,(14)/(2) )\\(1,7)`

Therefore, the center of the circle have coordinates of (1,7).

I hope this helps!