SOLUTION: Find the equation of the perpendicular bisector of the line segment joining P(7,-1) the Q(-3,5) with full steps.

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Question 1108685: Find the equation of the perpendicular bisector of the line segment joining P(7,-1) the Q(-3,5) with full steps.
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of the perpendicular bisector of the line segment joining P(7,-1) the Q(-3,5) with full steps.
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Step 1, find the slope of PQ
Step 2, find the midpoint of PQ

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The perpendicular bisector of a segment:
1) bisects the segment (meaning it passes through the midpoint of the segment)
2) is perpendicular to the segment (meaning that when you multiply the slopes of the perpendicular bisector and the line containing the segment, the result is -1 ).

The coordinates of the midpoint M%28x%5BM%5D%2Cy%5BM%5D%29
are the average of the coordinates of the end points, so
x%5BM%5D=%287%2B%28-3%29%29%2F2=4%2F2=2
y%5BM%5D=%28%28-1%29%2B5%29%2F2=4%2F2=2
So, the midpoint is M%282%2C2%29

The slope of the line containing segment PQ is
m%5BPQ%5D=%28-1-5%29%2F%287-%28-3%29%29=%28-6%29%2F%287%2B3%29=%28-6%29%2F10=-3%2F5 .
The slope of a perpendicular line is
m=%28-1%29%22%2F%22%28-3%2F5%29=%28-1%29%28-5%2F3%29=5%2F3

So, the perpendicular bisector of PQ is the line
with slope m=5%2F3 that passe through M%282%2C2%29 .
In point-slope form, based on point M ,
the equation of that line is
highlight%28y-2=%285%2F3%29%28x-2%29%29 .
That is just one of the infinitely many different forms of the equation of that line.
Solving for y ,
we find the one and only slope-intercept form of the equation of that line.
y-2=%285%2F3%29%28x-2%29
y-2=%285%2F3%29x-10%2F3%29
y=%285%2F3%29x-10%2F3%2B2
highlight%28y=%285%2F3%29x-4%2F3%29