Question

Show that the points A(3, 1), B(0, –2), C(1, 1) and D(4, 4) are the vertices of a parallelogram ABCD.

Answer 1

The points are A (3,1), B (0,-2), C(1,1)  and D (4,4)

Join AC and BD, intersecting at O.

We know that the diagonals of a parallelogram bisect each other. `"Midpoint of AC" = ((3+1)/2, (1+1)/2) = (4/2,2/2) = (2,1) `

`"Midpoint of BD " ((0+4)/2, (-2+4)/4) = (4/2,2/2) = (2,1)`

Thus, the diagonals AC and BD have the same midpoint

Therefore, ABCD is a parallelogram.