Question

The points $(7, -6)$ and $(-3, -4)$ are the endpoints of a diameter of a circle. What is the sum of the coordinates of the center of the circle?

a. $-4
b. $0
c. $2
d. $4

Answer 1

The center of the circle is (2, -5) and the sum of its coordinates is -3.

Step-by-step explanation:

To find the center of the circle, we need to find the midpoint between the two endpoints of the diameter. The midpoint formula is given by:

xm = (x1 + x2) / 2

ym = (y1 + y2) / 2

Substituting the coordinates of the endpoints, we get:

xm = (7 + (-3)) / 2 = 2

ym = (-6 + (-4)) / 2 = -5

Therefore, the coordinates of the center of the circle are (2, -5). The sum of the coordinates is 2 + (-5) = -3.