Question

Prove that quadrilateral A (-5,-4)B (1,-2)C(2,3)D(-4,1) is a parallelogram?.

Answer 1

See explanation...

Explanation:

Note that:

`vec(AB) = < 1-(-5), -2-(-4) > = < 6, 2 >`

`vec(DC) = < 2-(-4), 3-1 > = < 6, 2 >`

`vec(BC) = < 2-1, 3-(-2) > = < 1, 5 >`

`vec(AD) = < -4-(-5), 1-(-4) > = < 1, 5 >`

So `vec(AB) = vec(DC)` and `vec(BC) = vec(AD)`

So `ABCD` is a parallelogram.