Find the coordinates of the center

Question

A circle has a diameter with endpoints (-2,1) and (10,13). Find the coordinates of the center

Answer 1

use the midpoint formula to find the center since these points are the diameter endpoints (diameter is a line segment).

This works because the midpoint formula finds the middle point of the diameter, which it separate the length in half.

midpoint (x,y)

 

 

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

 

Y = (1+13)/2 = 7

 

 

the midpoint (or center of circle) = (4,7)

Answer 2

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

y = (1+13)/2= 7

so (4, 7)