What is the equation of the line that is perpendicular to the line passing through $(- 5, 3)$ $(-5,3)$ and $(4, 9)$ $(4,9)$ at midpoint of the two points?

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What is the equation of the line that is perpendicular to the line passing through $(- 5, 3)$ $(-5,3)$ and $(4, 9)$ $(4,9)$ at midpoint of the two points?

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Answer 1 · 2016-04-07T15:59:21

$y = - 1 \frac{1}{2} x + 2 \frac{1}{4}$ $y=-1 1/2x+2 1/4$

Explanation:

The slope a line that is perpendicular to a given line would be the inverse slope of the given line

$m = \frac{a}{b}$ $m = a/b$ the perpendicular slope would be $m = - \frac{b}{a}$ $m =-b/a$

The formula for the slope of a line based upon two coordinate points is

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2-y_1)/(x_2-x_1)$

For the coordinate points $(- 5, 3) and (4, 9)$ $(-5,3) and (4,9)$
$x_{1} = - 5$ $x_1 = -5$
$x_{2} = 4$ $x_2 = 4$
$y_{1} = 3$ $y_1 = 3$
$y_{2} = 9$ $y_2 = 9$

$m = \frac{9 - 3}{4 - (- 5)}$ $m = (9-3)/(4-(-5))$

$m = \frac{6}{9}$ $m = 6/9$

The slope is $m = \frac{6}{9}$ $m = 6/9$
the perpendicular slope would be the reciprocal (-1/m)
$m = - \frac{9}{6}$ $m = -9/6$

To find the midpoint of the line we must use the midpoint formula

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $((x_1+x_2)/2,(y_1+y_2)/2)$

$(\frac{- 5 + 4}{2}, \frac{3 + 9}{2})$ $((-5+4)/2,(3+9)/2)$

$(- \frac{1}{2}, \frac{12}{2})$ $(-1/2,12/2)$

$(- \frac{1}{2}, 6)$ $(-1/2,6)$

To determine the equation of the line use the point slope form
$(y - y_{1}) = m (x - x_{1})$ $(y-y_1)=m(x-x_1)$

Plug in the midpoint in order to find the new equation.
$(- \frac{1}{2}, 6)$ $(-1/2,6)$

$(y - 6) = - \frac{9}{6} (x - (- \frac{1}{2}))$ $(y-6)=-9/6(x-(-1/2))$

$y - 6 = - \frac{9}{6} x - \frac{9}{12}$ $y-6=-9/6x-9/12$

$ycancel(-6)cancel(+6)=-1 1/2x-3/4 +3$

$y=-1 1/2x+2 1/4$

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What is the equation of the line that is perpendicular to the line passing through $(- 5, 3)$ $(-5,3)$ and $(4, 9)$ $(4,9)$ at midpoint of the two points?

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Explanation:

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What is the equation of the line that is perpendicular to the line passing through (-5,3)(−5,3)(-5,3) and (4,9)(4,9)(4,9) at midpoint of the two points?

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What is the equation of the line that is perpendicular to the line passing through $(- 5, 3)$ $(-5,3)$ and $(4, 9)$ $(4,9)$ at midpoint of the two points?