How do you find the equation that is the perpendicular bisector of the line segment with endpoints $(-2, 4)$ and $(6, 8)$ ?

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Answer 1 · 2016-07-22T13:07:26

Equation of the perpendicular bisector: $y = -2x+10$

First we need to find the slope of the line joining these points:

$m = (y_2-y_1)/(x_2-x_1) = (8-4)/(6-(-2)) = 4/8 = 1/2$

The line perpendicular to this will have $m = -2$

We also need the co-ordinates of the midpoint.

$M((x_1+x_2)/2 ; (y_1+y_2)/2)$

$M((-2+6)/2 ; (4+8)/2)$

$M(2,6)$

Use the formula for slope and one point:
$y-y_1 = m(x-x_1)$

$y -6 = -2(x-2)$

$y = -2x+4+6$

Equation of the perpendicular bisector: $y = -2x+10$

How do you find the equation that is the perpendicular bisector of the line segment with endpoints (-2, 4)(-2, 4) and (6, 8)(6, 8)?