Given triangle ABC with vertices A(−3, 0), B (0, 6), and C(4, 6). Find the equations of the three perpendicular bisectors of the same triangle

Answer 1

I will do one, perpendicular bisector of AB

Midpoint = (-3+0 / 2 , 0 + 6 /2 ) = (-1.5, 3)

Slope = (6 - 0) / (0 - - 3) = 6 / 3 = 2

So slope of perpendicular is -1/2 (product of slopes = -1)

So perpendicular bisector y = -1/2 x + b passing through (-1.5, 3)

So 3 = -1/2 -1.5 + b

3 = 3/4 + b

b = 3 - 3/4 = 12/4 - 3/4 = 9/4

so y = -1/2 x + 9/4

For the other two use the same process