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

Answer:

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

Step-by-step 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:

$C(x,y) = \frac{1}{2}\cdot R_{1}(x,y)+ \frac{1}{2}\cdot R_{2}(x,y)$ (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:

$C(x,y) = \frac{1}{2}\cdot (-2,10)+\frac{1}{2}\cdot (6,-4)$

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

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

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