Using slopes. Prove that the points A(-2, -1), B(1,0), C(4, 3) and D(1, 2) are the vertices of a parallelogram.
The property of parallelogram states that opposite sides are equal.
We have 4 sides as AB,BC,CD,DA
Given points are A(-2,-1),B(1,0),C(4,3) and D(1,2)
AB and CD are opposite sides, and BC and DA are the other two opposite sides.
So slopes of AB = CD and slopes BC = DA
Slope of AB =
The slope of BC =
The slope of CD =
Slope of DA =
Therefore the Slope of AB = Slope of CD and
The slope of BC = Slope of DA
Also, the product of slope of two adjacent sides is not equal to -1, therefore it is not a rectangle.
Hence ABCD is a parallelogram.