Points A(5,-5), B(-5,5), C(1,7) and D(-7,-1) lie on the circle with equation x2+y2=50 show algebraically that AB is the perpendicular bisector of chord CD

Question

MATH URGENT PLEASE HELP THANKYOU!

Answer 1

Make a sketch...use graph paper if you need to.

Use the 2 point formula to write the equation of each of the 2 chords, AB and CD

To show that they are perpendicular the slope of the one must be the negative reciprocal of the slope of the other.

Then solve the 2 equations simultaneously. The solution must be the midpoint of CD if AB is the perpendicular bisector.

This solution involves a bunch of algebra...but is NOT difficult.