What is the center of the circle if the endpoints of the diameter are at (-12,-7) and (3,5)

Question

What is the center of a circle if the endpoints of the diameter are at (-12,-7) and (3,5)

Answer 1

Denise' method will give the midpoint, which is the center.

However, there is a midpoint formula based on the fact that

the center of two points is the average of the x and y values

 

Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2)

 

Midpoint of (-12,-7) and (3,5) is ((-12+3)/2, (-7+5)/2) = (-4.5, -1)

Answer 2

The center of your circle will be at the middle of the diameter, so you need to find the midpoint of the line that goes from one point to the other,  (3,5) is in quadrant I, the other is in quadrant 3.

 

If (X, Y) is the midpoint, than for the X coordinate value  X - 3 = -12 -X

For the Y coordinate value, Y - 5 = (-7 - Y)

 

Hint, when you solve these, the midpoint will have a negative value:)