SOLUTION: 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

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Question 1145517: 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
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Same problem.
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For side AB.
---
Step 1, find the midpoint. Do you know how to do that?
Step 2, find the slope of AB. Call it m
----
The slope of lines perpendicular is the negative inverse.
---> -1/m
Call that m2.
===============
Step 3, use y - y1 = m2*(x-x1) where (x1,y1) is the midpoint.
===================
Given triangle ABC with vertices A(−3, 0), B(0, 6), and C(4, 6).
a. Find the equations of the three medians of triangle ABC
Step 1, find the midpoints of the 3 line segments.
Step 2, find the equations of the 3 lines:
A to the midpoint of BC
B to the midpoint of AC
C to the midpoint of AB
===============
b. Find the equations of the three altitudes of the same triangle
Find the equations of the lines perpendicular to the AB, AC and BC thru the point C, B and A respectively.
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It's tedious and repetitious, but you get practice on how to do it.
I don't need the practice.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

One of the three equations you can find MENTALLY.


Notice that the side BC is horizontal, and its midpoint is M = (2,6).


Hence, the perpendicular bisector to this side is  x = 2.


By the way, this perpendicular bisector HAS NO SLOPE (!).


The slope is UNDEFINED in this case (!)


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