If (2,-7) and (8,15) are the endpoints of a diameter of a circle, what is the equation of the circle

To answer this, we need to know 2 things: the radius, and the center.

Let's start with the radius. Since the radius is half the diameter, we need to get the distance between the two given points. We do that with the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates from the points, we can substitute to make it:

d = √((8 - 2)^2 + (15 - -7)^2)

Now, we simplify

d = √(6^2 + 22^2)

d = √(36 + 484)

d = √520

d = 2√130

So, we know the diameter is 2√130, meaning the radius is √130.

Now, to find the center, we use (x1 + x2)/2, (y1 + y2)/2 for the coordinates.

Again, we can substitute.

(2 + 8)/2, (-7 + 15)/2

10/2, 8/2

5, 4

Now we know the center is (5, 4).

Finally, we can find the equation using (x – h)^2 + (y – k)^2 = r^2

(x - 5)^2 + (y - 4)^2 = 130

i got 10.28 but that rounds up to 10.3