Question

Which set of vertices forms a parallelogram?

A(2,4), B(3, 3), C(6, 4), D(5, 6)

A(-1, 1), B(2, 2), C(5, 1), D(4, 1)

A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)

A(-1, 2), B(1, 3), C(5, 3), D(1, 1)

Answer 1

Hints:

1. If opposite sides are parallel, the quadrilateral is a parallelogram.
Ex. check if AB//CD, and AD//BC
Use slope=\(\dfrac{y_2-y_1}{x_2-x_1}\)

or,

2. If opposite sides are equal, the quadrilateral is a parallelogram.
Ex. check if mAB=mCD and mAD=mBC
Use distance formula, distance=\(\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\)