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Question

Write an equation of the line described.

The perpendicular bisector of the segment joining (2,4) and (4,-4)

Solution

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Answered 2 years ago
Answered 2 years ago
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We have to find perpendicular bisector, we will use point-slope form yy1xx1=m\frac{y-y_1}{x-x_1} = m, where mm is a slope and (x1,y1)(x_1, y_1) on our bisector. First we know our bisector is perpendicular and that it is negative reciprocal of slope through points (2,4)(2, 4) and (4,4)(4, -4). Slope of the line through this points is 4442=4\frac{-4-4}{4-2} = -4, thus m=14m = \frac{1}{4}. Also, our bisector is passing through midpoint of our segment (2+42,442)=(3,0)(\frac{2+4}{2}, \frac{4-4}{2}) = (3, 0), so now from point-slope form we have that equation of our bisector is

yx3=14\frac{y}{x-3} = \frac{1}{4}

or in slope-intercept form y=14x34y = \frac{1}{4}x-\frac{3}{4}.

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