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

use the slope formula to find the slopes of the four sides; AB, BC. CD. and DA. Compare the slopes to verify that they are parallel.

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

slope = (y2-y1)/(x2-x1)

slope of ab = 3/-3 = -1
slope of cd = 3/-3 = -1

slope of bc = 2/6 = 1/3
slope of ad = 2/6 = 1/3

so both opp lines are ll