A diameter of a circle has endpoints P(-7, -4) and Q (3,2).

a. Find the center of the circle (hint: use midpoint formula).
b. Find the radius. If your answer is not and integer, express in radical form. (hint: use distance formula).
c. Write an equation for the circle.

Show work.

(This is 10th grade math, please don't make it advanced, shorten the steps).

3 answers

a. Using midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Midpoint = ((-7 + 3)/2, (-4 + 2)/2)
Midpoint = (-2, -1)

The center of the circle is (-2, -1).

b. Using distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((3 - (-7))^2 + (2 - (-4))^2)
Distance = sqrt(10^2 + 6^2)
Distance = sqrt(136)

The radius of the circle is sqrt(136).

c. The general equation for a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.

Plugging in the values from parts a and b:

(x - (-2))^2 + (y - (-1))^2 = (sqrt(136))^2
(x + 2)^2 + (y + 1)^2 = 136

The equation for the circle is (x + 2)^2 + (y + 1)^2 = 136.
AAAaannndd the bot gets it wrong yet again!
Use the distance to the center, not the other end of the diameter!

Distance = √((-2 - (-7))^2 + (-1 - (-4))^2) = √(5^2+3^2) = √34
so The equation for the circle is (x + 2)^2 + (y + 1)^2 = 34
Apologies for the error in the previous response, you are correct. The steps have been updated below:

a. Using midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Midpoint = ((-7 + 3)/2, (-4 + 2)/2)
Midpoint = (-2, -1)

The center of the circle is (-2, -1).

b. Using distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((-2 - (-7))^2 + (-1 - (-4))^2)
Distance = sqrt(5^2 + 3^2)
Distance = sqrt(34)

The radius of the circle is sqrt(34).

c. The general equation for a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.

Plugging in the values from parts a and b:

(x - (-2))^2 + (y - (-1))^2 = (sqrt(34))^2
(x + 2)^2 + (y + 1)^2 = 34

The equation for the circle is (x + 2)^2 + (y + 1)^2 = 34.