Find a perpendicular line that passes through the midpoint of $( 8 , - 12 )$ and $( 7,10 )$ .
A)
$4 y - 22 x + 59 = 0$
B)
$2 y - 4 x = 59$
C)
$44 y - 2 x + 59 = 0$
D)
$x - 22 y = 164$
E)
$22 x - y - 164 = 0$

Question

Find a perpendicular line that passes through the midpoint of $( 8 , - 12 )$ and $( 7,10 )$ . 
A)
 $4 y - 22 x + 59 = 0$ 
B)
 $2 y - 4 x = 59$ 
C)
 $44 y - 2 x + 59 = 0$ 
D)
 $x - 22 y = 164$ 
E)
 $22 x - y - 164 = 0$

Quizplus · Accepted Answer

First, we find the coordinates of the midpoint of the line segment that connects the given points:

Midpoint: $M = \left(\frac{8+7}{2},\frac{-12+10}{2}\right)=(7.5,-1)$

Next, we find the slope of the line that connects the given points:

$slope = \frac{10-(-12)}{7-8} = -22$

Since we want a line that is perpendicular to this line, we need to find its negative reciprocal:

$slope_{\perp} = \frac{1}{22}$

Now we can use the point-slope form of a line to find the equation of the line that passes through point $M$ with slope $slope_{\perp}$:

$y-(-1) = \frac{1}{22}(x-7.5)$

$22y + x - 59 = 0$

Which matches choice C).

Find a Perpendicular Line That Passes Through the Midpoint Of (8,−12)( 8 , - 12 )(8,−12)

Find a Perpendicular Line That Passes Through the Midpoint Of $( 8 , - 12 )$