Prove that points A(5, 1), B(2, 4), C(-4, 2) and D(-1, -1) represent the vertices of a parallelogram. Show all

Question

Prove that points A(5, 1), B(2, 4), C(-4, 2) and D(-1, -1) represent the vertices of a parallelogram. Show all your work and explain your solution.

Answer 1

Vector AB = (- 3 3)
Vector DC = (- 3 3) , Vector CD = (3 -3)
Vector BC = (- 6 - 2)
Vector AD = (- 6 -2) , Vector DA = (6 2)
AB + BC + CD + DA = 0
AB = DC
AD = BC

Opposite sides equal and parallel
Is a parallelogram.

Answer 2

You need to show slope of AB = slope of CD, and slope of AD = slope of BC. If you show that then you fhave shown that the opposite sides are parallel and thus the quadrilateral is a ||-ogram. Slope AB = (4-1)/(2-5) = -1 Slope CD = (-1-2)/(-1+4) = -1 Thus AB || CD Now you should be able to finish this.

Answer 3

Get the slopes of the four sides by evaluating (y2-y1)/(x2-x1) for each. The slopes of the opposite sides will match iff the thing is a parallelogram.