Question

If the centre of a circle is ($\frac{4}{3}$, - 2) and one of the diameter is (3,2), then find the coordinates of the other end.

Answer 1

Given center of the circle $(\frac{4}{3},-2)$ and one extremity of the diameter is $(3,2)$. Say the other extremity is $(h,k)$. Then the center of the circle should be the midpoint of $(3,2)$ & $(h,k)$

$\therefore$ $(\frac{4}{3},-2)=(\frac{3+h}{2},\frac{K+2}{2})$

$\therefore$ $\frac{3+h}{2}=\frac{4}{3}$

$\Rightarrow 9+3h=8$

$\Rightarrow h=-1/3$

Similarly,

$\frac{K+2}{2}=-2$

$\Rightarrow K=-6$

$\therefore$ the other extremity is $(-1/3,-6)$