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Find an equation for the perpendicular bisector of the line segment whose endpoints are (5, 5) and ( 7, 1).​

User Stormbeta
by
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1 Answer

6 votes

Answer:

x -2y = 0

Explanation:

A perpendicular bisector is a line perpendicular to a given line or segment that goes through the midpoint between given points. The perpendicular line will have a slope that is the opposite reciprocal of the slope of the segment between the given points.

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The midpoint between A and B is ...

M = (A +B)/2

M = ((5, 5) +(7, 1))/2 = (12, 6)/2 = (6, 3)

The slope of the line between A and B is ...

m = (y2 -y1)/(x2 -x1)

m = (1 -5)/(7 -5) = -4/2 = -2

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The opposite reciprocal of the slope of the given segment is ...

m' = -1/-2 = 1/2

The point-slope form of the equation of the perpendicular bisector can be written as ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

y -3 = 1/2(x -6) . . . . line with slope 1/2 through point (6, 3)

Multiplying by 2 gives ...

2y -6 = x -6

Subtracting (2y -6) gives the standard-form equation ...

x -2y = 0

Find an equation for the perpendicular bisector of the line segment whose endpoints-example-1
User Massimo Zerbini
by
7.1k points

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