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:

`((x_1+x_2)/(2)),((y_1+y_2)/(2))`

So,

`\begin{gathered} (2+x)/(2)=5 \\ 2+x=10 \\ x=10-2 \\ x=8 \end{gathered}`

and

`\begin{gathered} (5+y)/(2)=1 \\ 5+y=2 \\ y=2-5 \\ y=-3 \end{gathered}`

Hence the midpoint is (8, -3)