Question

Which point lies on a circle that is centered at A(-3, 2) and passes through B(1, 3)?

Answer 1

if the circle's CENTER is at (-3,2) any point on the circle will be at a distance of "radius" from the center, that is

Answer 2

so just find the distance between A and B to get the radius and compare with other points, the distance must be the same for any other point on the circle

\(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ -3}}\quad ,&{\color{blue}{ 2}})\quad B&({\color{red}{ 1}}\quad ,&{\color{blue}{ 3}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 3

thank you jdoe

Answer 4

yw

Answer 5

do you know what point the circle lies on

Answer 6

hhmmm what did you get for the distance anyway?

Answer 7

I got 2.25

Answer 8

hmmm \(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ -3}}\quad ,&{\color{blue}{ 2}})\quad B&({\color{red}{ 1}}\quad ,&{\color{blue}{ 3}})
\end{array}\qquad
d = \sqrt{({\color{red}{ 1}}-{\color{red}{ -3}})^2 + ({\color{blue}{ 3}}-{\color{blue}{ 2}})^2} \ne 2.25\)

Answer 9

notice that (1 - (-3)) => 1+3