Find the equation of the perpendicular line passing through the midpoint of the line segment connecting (−2, 5) and (7, −3)

Question

Calc 1 Homework Question

Answer 1

The slope is opposite, reciprocal.

 

(-3 - 5)/(7 - (-2))

-8/9

 

So, the slope is 9/8.

 

-8/2 = -4

9/2 = 4 1/2

 

Midpoint is (4 1/2, 4).

 

y - 4 = (9/8)(x - 9/2)

y - 4 = (9/8)x - 81/16

y = (9/8)x - 17/16

Answer 2

midpoint:  ((-2+7)/2, (5-3)/2) = (5/2, 1)

Slope: m = (-3-5)/(7-(-2)) = -8/9

perpendicular slope = -1/m = 9/8

 

equation of line through (5/2, 1) with slope 9/8

 

y = mx + b

use (5/2, 1) as (x, y) with m=9/8.  Find b.

1 = (9/8)(5/2) + b

1 = 45/16 + b

b = 1 - 45/16

b = -29/16

 

y = (9/8)x - 29/16

 

You can clear the fractions if you wish by

multiplying through by 16, but the above 

equation is the slope intercept form of

the answer.

16y = 18x - 29

-18x + 16y = -29