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kiruha [24]
3 years ago
9

Find an equation for the perpendicular bisector of the line segment whose endpoints are (5,-9) and (1,3).

Mathematics
1 answer:
____ [38]3 years ago
3 0

Given coordinates of the endpoints of a line segment  (5,-9) and (1,3).

In order to find the equation of perpendicular line, we need to find the slope between given coordinates.

Slope between (5,-9) and (1,3) is :

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

m=\frac{3-\left(-9\right)}{1-5}

m=-3

Slope of the perpendicular line is reciprocal and opposite in sign.

Therefore, slope of the perpendicular line = 1/3.

Now, we need to find the midpoint of the given coordinates.

\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)

=\left(\frac{1+5}{2},\:\frac{3-9}{2}\right)

=\left(3,\:-3\right)

Let us apply point-slope form of the linear equation:

y-y1 = m(x-x1)

y - (-3) = 1/3 (x - 3)

y +3 = 1/3 x - 1

Subtracting 3 from both sides, we get

y +3-3 = 1/3 x - 1 -3

<h3>y = 1/3 x - 4 .</h3>
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