Question

If the parallel sides of a trapezoid contained by the lines y = -x + 5 and y = -x - 9, what equation represents the line contained by the midsegment?

Answer 1

Hello,

Let's take a point of d:y=-x+5
if x=0 then y=5 : A=(0,5)
The perpendicular of d passing through A is
y-5=1(x-0) since the slope is -1*?=-1==>?=1
y=x+5
Intersection with the line d':y=-x-9 is

y=x+5 and y=-x-9 ==>x+5=-x-9==>2x=-14==>x=-7 and y=-7+5=-2
B=(-7,-2)
The middle of [AB] is C=((0+(-7))/2,(5+(-2))/2)=(-3.5,1.5)

The line parallele at d passing through C is
y-1.5=-1(x+3.5)==>y=-x-2