A quadrilateral has the vertices at the points `(-4,2),\ (2,6),\ (8,5)\ a n d\ (9,-7)` . Show that the mid points of the sides of this quadrilateral are the vertices of a parallelogram.

Explanation

Let the vertices of quadri lateral be `P(-4,2,`, `Q(2,6) R(8,5)` and `S(9,-7)` Let `A, B, C` and `D` are the med points `P(-4,2)` and `Q(2,6)` `P(-4,2)` and `Q(2,6)`


`therefore` Coordinates of `A` are `(frac{-4+2}{2}, frac{2+6}{2})=(frac{-2}{2}, frac{8}{2})=(-1,4)`


Coordinates of `B` are


`(frac{2+8}{2}, frac{6+5}{2})=(frac{10}{2}, frac{11}{2})=(5, frac{11}{2})`


Coordinates of `c` are
`(frac{8+9}{2}, frac{5-7}{2})=(frac{17}{2}, frac{-2}{2})=(frac{17}{2},-1)`


coordinates of `D` are `(frac{9-4}{2}, frac{7+2}{2})=(frac{5}{2}, frac{-5}{2})` distance between `A` and `B`.



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