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

$\frac{y}{x-3} = \frac{1}{4}$

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

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