posted by Emily .
triangle ABC is an isosceles right triangle. The endpoints of the hypotenuse of ABC are A(4,7)B(8,1). Find the possible coordinates for the vertex C
The C willbe on the line which is the perpendicular bisector of the hypotenuse.
slope of AB= (6/-4)
slope of bisector= 4/6
but a point on the bisector is (6,4)
y= 4/6 x + b
4= 4/6 *6+b
equation of bisector is y= 4/6 x
now, there is a point on that line which forms to line segments which are 90 deg to each other.
Now, if AC and BC are perpendicular the slopes are neg reciprocals.
slope AC= (7-4x/6)/(4-x)
slope BC= (8-4x/6)/(1-x)
these are neg reciprocals, so this leads to
solve for x. It looks a little messy.
combine terms, simplify, solve for x with the binomial equation.