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?

1 Answer
Apr 7, 2016

y=-1 1/2x+2 1/4y=112x+214

Explanation:

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

m = a/bm=ab the perpendicular slope would be m =-b/am=ba

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

m = (y_2-y_1)/(x_2-x_1)m=y2y1x2x1

For the coordinate points (-5,3) and (4,9)(5,3)and(4,9)
x_1 = -5x1=5
x_2 = 4x2=4
y_1 = 3y1=3
y_2 = 9y2=9

m = (9-3)/(4-(-5))m=934(5)

m = 6/9m=69

The slope is m = 6/9m=69
the perpendicular slope would be the reciprocal (-1/m)
m = -9/6m=96

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

((x_1+x_2)/2,(y_1+y_2)/2)(x1+x22,y1+y22)

((-5+4)/2,(3+9)/2)(5+42,3+92)

(-1/2,12/2)(12,122)

(-1/2,6)(12,6)

To determine the equation of the line use the point slope form
(y-y_1)=m(x-x_1)(yy1)=m(xx1)

Plug in the midpoint in order to find the new equation.
(-1/2,6)(12,6)

(y-6)=-9/6(x-(-1/2))(y6)=96(x(12))

y-6=-9/6x-9/12y6=96x912

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

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