A quadrilateral has vertices `(4,1), (1,7),(-6,0)` AND `(-1,-9)`. Show that mid-points of the sides of this quadrilateral form a parallelogram.

Explanation

Let` A(4,1`), `B(1,7)`, `C(-6,0)` and `D(-1,-9)` be the vertices of the given quadrilateral.

Let P, Q, R and S be the mid-points of A B, B C, C D and D A, respectively.

So, the coordinates of P, Q, R and S are

`P(frac[5]2, 4), Q(frac[-5]2, frac[7]2), R(frac[-7]2, frac[-9]2)` and` S(frac[3]2,-4).`

In order to prove that PQRS is a parallelogram, it is sufficient to show that PQ is parallel to R S andPQ is equal to R S.

Now, we have,

Slope of PQ


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