Question

Circle P has a diameter with end points at (-4,3) and (1,6). Find the center of the circle.

Answer 1

The center is the midpoint of the diameter.

The coordinates of the midpoint:
$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$
(x₁,y₁) - the coordinates of one endpoint
(x₂,y₂) - the coordinates of the other endpoint

$(-4,3) \\ x_1=-4 \\ y_1=3 \\ \\ (1,6) \\ x_2=1 \\ y_2=6 \\ \\ \frac{x_1+x_2}{2}=\frac{-4+1}{2}=\frac{-3}{2}=-1.5 \\ \frac{y_1+y_2}{2}=\frac{3+6}{2}=\frac{9}{2}=4.5$

The coordinates of the center are (-1.5,4.5) - the answer is A.