Question

If the diameter of a circle has endpoints A(7, 2) and B(-1, 8), where is the center of the circle?
C(4, 3)
D(3, 5)
E(9, 12)
F(5, 8)
G(4, 5)

Answer 1

The midpoint of segment AB is the center of the circle

Answer 2

Use the midpoint formula to find the midpoint of AB

Answer 3

\(\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 7}}\quad ,&{\color{blue}{ 2}})\quad &({\color{red}{ -1}}\quad ,&{\color{blue}{ 8}})
\end{array}\qquad
\left(\cfrac{{\color{red}{ x_2}} + {\color{red}{ x_1}}}{2}\quad ,\quad \cfrac{{\color{blue}{ y_2}} + {\color{blue}{ y_1}}}{2} \right)\)

Answer 4

The midpoint is (3, 5)

Answer 5

correct

Answer 6

so that's the center of the circle

Answer 7

then that's where the center of the circle is