A circle has a center at (1/2,2). If one endpoint of the is (-5,7), what are the coordinates of the other endpoint?

Question

A.(-11/2,9/2)

B.(6,-3)

C.(-9/2,9/2)

D.(4,-2)

Answer 1

The centre of a circle is the midpoint of the diameter. The midpoint of the line between two points has coords which are the average of the coords of the endpoints. If the other end of the diameter is (x,y) then the average of the endpoints is ½(x-5) and ½(y+7) so ½(x-5)=½ and ½(y+7)=2.

So x-5=1 and x=6, and y+7=4, and y=-3, so the coords of the other end of the diameter are (6,-3), answer B.