Question

The coordinates of the vertices of a quadrilateral ABCD are A (3,1), B(11, -3), C(10,3) and D(6,5). Prove that ABCD is a trapezoid.

Answer 1

We need to prove the DC and AB are parallel to each other and AD and DC are perpendicular because those features make the quadrilateral a trapezoid.

Answer 2

Parallel lines have the same slope:
Slope of DC-> -1/2
Slope of AB -> -1/2
Thus, line AB is parallel to line DC

Answer 3

Perpendicular lines have slopes that are negative reciprocals:
Slope of AD -> 2
Slope of DC ->-1/2
Thus, line AD and line DC are perpendicular to each other

Answer 4

Beautiful explanation. Thanks!

Answer 5

No problem! :)