Question

A circle has a diameter with endpoints of (-3, 8) and (7, 4). What is the center of the circle? (10, 12) (5, 12) (2, 6)

Answer 1

Centre point of the circle is

= ( -3+7)/2 , (8+4)/2.

= 2, 6

Answer 2

The center of the circle whose diameter with endpoints (-3, 8) and (7, 4) is (2, 6)

Solution:

Given, a circle has a diameter with endpoints of (-3, 8) and (7, 4).  

We have to find What is the center of the circle?  

We know that, center is the midpoint of endpoints of diameter.

Now, center point of the circle= midpoint of (-3, 8) and (7, 4).

Midpoint of $\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { and }\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right) \text { is }\left(\frac{\mathrm{x}_{1}+\mathrm{x}_{2}}{2}, \frac{\mathrm{y}_{1}+\mathrm{y}_{2}}{2}\right)$

$\text { Center point of circle }=\left(\frac{-3+7}{2}, \frac{8+4}{2}\right)$

$= (\frac{4}{2}, \frac{12}{2}) = (2, 6)$

As we can see that, the answer we have got is third option.  

Hence, third option (2, 6) is the centre point of circle.