Find the center of the circle with a diameter that has endpoints ( − 9 , 6 ) and ( 9 , − 7 ) .

Question

Find the center of the circle with a diameter that has endpoints(-9,6) and (9,−7).

Answer 1

The center of a circle is the midpoint of its diameter; in this problem, the midpoint between the two endpoints of the diameter - i.e. find the midpoint of the line segment with endpoints (-9, 6) and (9, -7) which is (average of x values, average of y values) => ((-9+9)/2, (6-7)/2) => (0, -1/2).

Answer 2

center is the midpoint of the two endpoints (0,-1/2)

Just average the coordinates of the endpoints

(-9+9)/2 = 0/2 = 0

(6-7)/2 = -1/2

if you want the equation for the circle also find the radius

radius is half the diameter

diameter = the distance between the two endpoints

use the distance formula, a version of the Pythagorean Theorem

diameter = sqr((-9-9)^2 + (-7-6)^2

= sqr(18^2+13^2) = sqr493

radius = sqr493/2

radius squared = 493/4

the circle is (x-h)^2+(y-k)^2 = r^2

where (h,k) = the center = (0,-1/2),

r^2 = 493/4

(x-h)^2 +(y--1/2)^2 = 493/4

x^2 + (y+1/2)^2 = 493/4

x^2 +y^2 +y+1/4 = 493/4

multiply by 4

4x^2 +4y^2 +4y +1= 493

4x^2+4y^2 +4y = 492