Question

if the coordinates of the diameter of a a circle are (4,3) and (2,1), what is the coordinates of its centre?

Answer 1

Centre will be the midpoint of the line joining the given points.

Using Midpoint Rule,

$x = \frac{x1 + x2}{2} ,\: y = \frac{y1 + y2}{2} \\ x = \frac{4 + 2}{2} , \: y = \frac{3 + 1}{2} \\ x = \frac{6}{2} ,\: y = \frac{4}{2} \\ x = 3,\: y = 2$

Thus, the co-ordinates of the centre is (3,2)

Answer 2

Answer:

centre of the circle divide the line joining the given points in 1:1

use formula for find mid point of line...

co ordinates of centre = x1 +x2/2 , y1 +y2/2

centre = (4+2)/2 , (3+1)/2

= (3,2)

thus (3,2) is the coordinates of its centre...