Question

If the endpoints of the diameter of a circle are (7, 8) and (-2, 12), what are the coordinates of the center of the circle?

Answer 1

centre = `(5/2 , 10 )`

Explanation:

The centre of the circle is at the mid-point of the diameter. Hence to find coords of centre , find the mid-point of the end points.

hence :`[ 1/2 (x_1 + x_2 ) , 1/2(y_1 + y_2 ) ]`

let `(x_1 , y_1 ) = ( 7 , 8 )color(black)(" and ") (x_2 , y_2 ) =(-2 , 12 )`

substitute these values into the formula:

`rArr[ 1/2(7-2) , 1/2(8+12 )] = ( 5/2 , 10 )`