Question

What for formula do I use for: ???

a) If the diameter of a circle has endpoints at (-2, 4) and (3, 8), what is the length of the radius of the circle?

b)If the endpoints of the diameter of a circle are (-10, 12) and (12, 18), what are the coordinates of the center of the circle?

Answer 1

find the distance between both points and, that'd be the diameter, recall that the radius is half the diameter \(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 4}})\quad &({\color{red}{ 3}}\quad ,&{\color{blue}{ 8}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 2

@jdoe0001 So I go square root of 41! So if the radius is half would it be square root of 20.5?

Answer 3

yeap

Answer 4

the coordinates of the center, will be half-way between the distance between those 2 points

thus, the center will be the MidPoint of (-10, 12) and (12, 18) thus \(\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ -10}}\quad ,&{\color{blue}{ 12}})\quad &({\color{red}{ 12}}\quad ,&{\color{blue}{ 18}})
\end{array}\qquad
\left(\cfrac{{\color{red}{ x_2}} + {\color{red}{ x_1}}}{2}\quad ,\quad \cfrac{{\color{blue}{ y_2}} + {\color{blue}{ y_1}}}{2} \right)\)

Answer 5

@jdoe0001 I'm having trouble finding:
If the endpoints of the diameter of a circle are (-10, 12) and (12, 18), what are the coordinates of the center of the circle?