Question

The end points of the diameter of a circle are ( 2,4) and ( -3 , -1 ) .Find its center.

Answer 1

A(2,4) ---------•--------- B(-3,-1)

$\:\:\:\:\:\:\:\:\:\:\: {C(x,y)}$

Using midpoint formula

$\sf{x = \dfrac{x1 + x2 }{2}}$

$\sf{x = \dfrac{2 + (-3) }{2}}$

$\pink\sf{x = \dfrac{-1}{2}}$

And,

$\sf{y = \dfrac{y1 + y2 }{2}}$

$\sf{x = \dfrac{4 + (-1) }{2}}$

$\sf{x = \dfrac{3 }{2}}$

Therefore , Co-ordinate of Center (C) is ($\sf\dfrac{-1}{2} , \dfrac{3}{2}$)