Question

1. Show that ABCD is a trapezoid.
(A: (-2, 5); B: (4, 5); C: (6,2); D: (2, -1)).

2. Write an equation in slope-intercept form for the line that passes through (5,0) and is perpendicular to the line given by y = -5/2x + 6.

Answer 1

2)
m = 2/5

y = mx + b

0 = (2/5)(5) + b

0 = 2 + b
b = -2

y = 2x/5 -2

Answer 2

in a trapezoid, one pair of opposite sides are parallel
Make a sketch

slope BC = (5-2)/(4-6) = 3/-2 = - 3/2
slope AD = (5-(-1))/)-2-2) = 6/-4 = -3/2

Yup, it is

I didn't check for the other pair
I could see that AB is horizontal, since both points have the same y value, which was not true for DC

Answer 3

How do I show that ABCD is a trapezoid, then?

Answer 4

AB = (5-5) /(4-(-2) = 0/6 = 0
AB is horizontal

BC = (2-5)/(6-4) = -3/2

CD = (-1-2)/(6-2) = -3/4

CD is not true

AD = (-1-5)/(2-(-2) = -6/4 = -3/2

So one pairs