Question

AB¯ is the diameter of circle T. Point A is located at (-4,2) and point B is located at (2,-8). What are the coordinates of the center of this circle?

Answer 1

Centre is at the middle or the midpoint of the diameter.

And the formula of midpoint is

$( \frac{x_{1} +x_{2}}{2},\frac{y_{1} +y_{2}}{2})$

For the given question, x1=-4, y1=2, x2=2, y2=-8

So we will get

$( \frac{-4+2}{2}, \frac{2-8}{2} ) = (-1, -3)$

And that's the required centre .

Answer 2

Answer:  The required co-ordinates of the center of the circle are (-1, -3).

Step-by-step explanation:  Given that AB is the diameter of circle T. The co-ordinates of point A are (-4, 2) and the co-ordinates of point B are (2, -8).

We are to find the co-ordinates of the center of this circle.

We know that

the center of a circle is the mid-point of any of its diameter.

The co-ordinates of the midpoint of a line segment with endpoints (a, b) and (c, d) are given by

$\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right).$

Therefore, the co-ordinates of the midpoint of diameter AB are

$\left(\dfrac{-4+2}{2},\dfrac{2-8}{2}\right)\\\\\\=\left(\dfrac{-2}{2},\dfrac{-6}{2}\right)\\\\=(-1,-3).$

Thus, the required co-ordinates of the center of the circle are (-1, -3).