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how to figure out the equation of the perpendicular bisector of a line when the end points of the line are given?

how to figure out the equation of the perpendicular bisector of a line when the end-example-1
User Val Kornea
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First find the equation of the line, Ill use the first one as an example:

(-5,10) , ( -9,2)

To work out the gradient:

(y_2 - y_1)/(x_2 - x_1)

(2 - 10)/(-9 - -5) = (-8)/(-4) = 2

So the gradient of the line is 2

The midpoint of the line is
( (-5 + -9)/(2), (10+2)/(2)) = ( -3.5, 6)
The gradient of the inverted line is -0.5 as it is the negative reciprocal of the gradient of the first line.
Here, we work out the equation of the bisector.

y-6 = -0.5(x+3.5)

y-6 = (-x)/(2)-1.75

y = -(1)/(2) x+4.25
User Edward Louth
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