Question

A diameter of a circle has enpoints (-2, 10) and (6, -4) in the standard (x, y) coordinate plane. What is the center of the circle?

Answer 1

The center of the circle is
`C(x,y) = (2, 3)`.

Explanation:

The center of the circle is the midpoint of the segment between the endpoints. We can determine the location of the center by this vectorial expression:

`C(x,y) = (1)/(2)\cdot R_(1)(x,y)+ (1)/(2)\cdot R_(2)(x,y)` (1)

Where:

`C(x,y)` - Center.

`R_(1) (x,y)`,
`R_(2) (x,y)` - Location of the endpoints.

If we know that
`R_(1) (x,y) = (-2,10)` and
`R_(2) (x,y) = (6,-4)`, then the location of the center of the circle is:

`C(x,y) = (1)/(2)\cdot (-2,10)+(1)/(2)\cdot (6,-4)`

`C(x,y) = (-1, 5) + (3, -2)`

`C(x,y) = (2, 3)`

The center of the circle is
`C(x,y) = (2, 3)`.