Question

Triangle with vertices:
D(-18,12)
E(-6,-12)
F(12,6)

Show that the right bisectors of the sides of triangleDEF all intersect at point C(-4,4), the circumcentre of the triangle.

-I found the midpoint of DF then the slope of the midpoint and point E, then found y intercept of new point (midpoint I labelled A) I then subbed point C into the equation of the line found. But it doesn't seem to be equally each other as they should...help!

Answer 1

Problem #1 is that you are not finding the right-bisector, but rather the medians

I will describe the steps to find your first right-bisector
1. the midpoint of DF is A(-3, 9)
2. slope of DF = 6/-30 = - 1/5
3. So the slope of the right-bisector of DF is +5
4. equation of right-bisector is
y = 5x + b , but A(-3,9) lies on it, so
9 = 5(-3) + b
b = 24
right-bisector of DF is y = 5x + 24

repeat those steps for one of the other sides

solve those two equations, you should get (-4,4)

Find the equation of the third side, using the above steps
Sub in (-4,4) to see if it satisfies the third equation, it should !!

Answer 2

Thanks!!