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

A(-1.5, 4.5)
B(1,2)
C(0,0)

D, (-2.5, -1.5)

Verified Answer :

naǫ

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.

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