If a circle has a diameter with endpoints (-2, -5) and (3, 4), then what is the center of the circle... The radius of the circle?

Answer 1

Hello Bri,

The standard form for a circle is (x - h)² + (y - k)² = r², where the center is (h, k).

The center of the circle will be the midpoint of the points given. That is,

h = (-2 + 3) / 2 = 1/2 = .5 and

k = (-5 + 4) / 2 = -1/2 = -.5,

→ (h, k) = (.5, -.5).

Now, the x and y in the equation represent points ON the circle, so you can pick either of the given points. I am going to use (3, 4)

→ (3 - 1/2)² + (4 - (-1/2))² = r², from which you can solve for r²,

→ 25/4 + 81/4 = r²

→ 106/4 = r²

→ r = (√106)/2

If the question had asked for the equation of the circle, just plug in the h, k, and r²

→ (x - .5)² + (y - (-.5))² = 26.5

→ (x - .5)² + (y + .5)² = 26.5.

Thank you for the question, and have a great evening!

Michael Ehlers

Answer 2

The is the midpoint of the diameter; the co-ordinates of the center are the averages of the co-ordinates of the endpoints.

The radius is 1/2 the distance from the ends of the diameter; the length of the diameter is found from the distance formula applied to the endpoints of the diameter.

The distance between two points (x,y) and (s,t) is sqrt[(x-s)² + (y-t)²].