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

step-by-step explanation:

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).