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

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((a+c)/(2),(b+d)/(2)\right).`

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

`\left((-4+2)/(2),(2-8)/(2)\right)\\\\\\=\left((-2)/(2),(-6)/(2)\right)\\\\=(-1,-3).`

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

Answer 2

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

And the formula of midpoint is

`( (x_(1) +x_(2))/(2),(y_(1) +y_(2))/(2))`

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

So we will get

`( (-4+2)/(2), (2-8)/(2) ) = (-1, -3)`

And that's the required centre .