Question

18. the diameter of a circle has endpoints P(-10,-2) and Q(4,6).
A find the center of the circle
b. find the radius. If you answer is not an integer, express it in radical form.
c. write an equation for the circle. (3 points)
I really need help on this I have no clue what im doin I will fan and medal

Answer 1

Since the diameter is a straight line through the middle, and you have the coordinates of its, endpoints, you can tell how many units long it is. The two x coordinates are -10 and 4, so the diameter is 14 units long. The radius is half that (7).

Answer 2

To find the center, we use the equation \[(x-h)^{2}+(y-k)^{2}=r ^{2}\] with (h,k) being the center. The midpoint of those two endpoints is the center, as well.

Answer 3

To find the midpoint, we add the two x coordinates and then divide them by 2. We do the same with the y coordinates.

Answer 4

Using the numbers you give, the center would be (-3, -2).

Answer 5

We can then plug that into the equation. You can use either of the endpoints as x and y

Answer 6

Then you just solve the equation for \[r ^{2}\] and you have all the answers!

Answer 7

^_^ thank you so much that helped a lot I believe I get it now

Answer 8

You're welcome! :)