Question

If the coordinates of one end of a diameter of a circle are (2,3) and the coordinates of its centre are (-2,5), then the coordinates of the other end of the diameter are

(a) (-6,7) (b) (6, -7) (c) (4, 2) (d) (5, 3)

Answer 1

Let the diameter be AB whose coordinates of centre is (-2,5) and the coordinates of B are (2,3).

Let the coordinates of A be (x,y).

Mid-point of AB is (-2,5), which is the centre of the circle. using midpoint formula C (-2, 5) = (x , y)

$\to$ (-2,5) = $\frac{x+2}{2}$, $\frac{y+3}{2}$

here $\frac{x+2}{2}$ = -2 and $\frac{y+3}{2}$= 5

or $x+2=-4$ and $y+3=5$1

$x=-6andy=7$

Therefore, the coordinates of A are $(-6,7)$

Answer :- (a) (-6,7)