SOLUTION: Find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector ℓ of segment AB. A(−4, 7), B(8, −13)

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Question 992589: Find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector ℓ of segment AB.
A(−4, 7), B(8, −13)
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
Any pt. on perpendicular bisector of a line segment is equidistant from both the end points.
So, Distance from P to A = Distance from P to B
=> sqrt%28%28x%2B4%29%5E2%2B%28y-7%29%5E2%29+=+sqrt%28%28x-8%29%5E2%2B%28y%2B13%29%5E2%29
Squaring both sides, & simplifying,
x%5E2%2By%5E2%2B8x-14y%2B65+=+x%5E2%2By%5E2-16x%2B26y%2B233
=> 24x-40y-168+=+0
=> 3x-5y-21+=+0 represents all such points P as required.