Question

A circle in the standard (x,y) coordinate plane has

Answer 1

Given:

Center of a circle is at point C(-1,2).

AB is the diameter of the circle.

Coordinates of the point A are A(2,6).

To find:

The coordinates of point B.

Solution:

Let the coordinates of point B are (a,b).

If AB is the diameter of the circle, then A and B are end points of diameter of the circle and the center C is the midpoint of AB.

$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

Point C = Midpoint of AB

$(-1,2)=\left(\dfrac{2+a}{2},\dfrac{6+b}{2}\right)$

On comparing both sides, we get

$\dfrac{2+a}{2}=-1$

$2+a=-1\times 2$

$a=-2-2$

$a=-4$

Similarly,

$\dfrac{6+b}{2}=2$

$6+b=2\times 2$

$b=4-6$

$b=-2$

Therefore, the coordinates of point B are (-4,-2).