Question

4. The center of a circle has a center of (5, 1), and an endpoint of the diameter of the circle is (2,5). What are the coordinates of the other endpoint of the diameter?

Answer 1

Let the other end point be (x,y)

THe two endpoints are in a straight line where the Center would be the MIDPOINT of them.

Thus, we can say

(2, 5) ----------- (5,1) ----------- (x,y)

We can use midpoint formula here, which is:

Midpint Formula:

$(\frac{x_1+x_2}{2}),(\frac{y_1+y_2}{2})$

So,

$\begin{gathered} \frac{2+x}{2}=5 \\ 2+x=10 \\ x=10-2 \\ x=8 \end{gathered}$

and

$\begin{gathered} \frac{5+y}{2}=1 \\ 5+y=2 \\ y=2-5 \\ y=-3 \end{gathered}$

Hence the midpoint is (8, -3)