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Prove that the points (–2, –1), (1, 0), (4, 3) and (1, 2) are the vertices of a parallelogram. Is it a rectangle ?

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#### Solution

Let the given point be A, B, C and D respectively. Then,

Coordinates of the mid-point of AC are

`( \frac{-2+4}{2},\ \frac{-1+3}{2} )=(1,1)`

Coordinates of the mid-point of BD are

`( \frac{1+1}{2},\ \frac{0+2}{2})=(1,1)`

Thus, AC and BD have the same mid-point. Hence, ABCD is a parallelogram.

Now, we shall see whether ABCD is a rectangle or not.

We have,

`AC=sqrt((4-(-2))^{2}+(3-(-1))^{2})=2 `

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

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