Question

If coordinates of the centre and one end of a diameter of a circle are $(7,3)$ and $(5,-7)$ respectively, then the coordinates of the other end of the diameter are

• A. $(6,-2)$
• B. $(9,13)$
• C. $(12,-4)$
• D. $(-2,6)$

Answer 1

The correct option is B $(9,13)$

Let $A\equiv (5,-7),C\equiv (7,3)$
Let $B(x,y)$ be the other end of the diameter.
We know that in a circle, the centre bisects the diameter, so $C$ is midpoint of $AB$.
$(7,3)=(\frac{5+x}{2},\frac{-7+y}{2})\Rightarrow x=9,y=13\therefore B\equiv (9,13)$