Points/ endpoints of a circle

Question

the endpoints of the diameter of a circle are D(7, -2) and E(11, -8).
a) Determine the coordinates of the the centre of the circle. 
b) Determine the length of the circle's radius

Answer 1

a) Use the midpoint formula to determine the Center [note: the Center is the midpoint of the diameter segment]

 

      C = M =  (  (x₁+x₂)/2.  (y₁+y₂)/2 )

            C = ( (7+11)/2, (-2-8)/2 )

            C = (9,-5)

 

The radius is distance (use distance formula) from the Center of the circle (point C) to either endpoint of the diameter [either point D or point E].

 

    r = √( (x₂-x₁)² + (y₂ - y₁)² )

    r = √( (9-7)² + (-5-(-2))² )

    r = √( 4 + 9)

    r = √13