214. Prove (hat the points (-2, -1), (1, 0), (4, 3) and (1, 2) are the vertices of a parallelogram is it a rectangle?

Let A(-2,-1), B(1, 0), C(4, 3) and D(1, 2) be the vertices of a parallelogram
Now, the mid-point of diagonal AC is

Here, we have
x₁ = 2,    y₁ = —1
x₂ = 4,    y₂ = 3



The mid-point of diagonal BD

[Here, we have
x₁ = 1,    y₁ = 0
x₂ = 1,    y₂ = 2]

∴ The mid-point of AC is the same as the midpoint of BD.
∆ ABCD is a parallelogram.
Test for Rectangle :

Clearly AC ≠ BD
So, ABCD is not a rectangle.