Question

Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.

Answer 1

The distance d between two points and is given by the formula

In a parallelogram the opposite sides are equal in length.

Here the four points are A(1, −2), B(3, 6), C(5, 10) and D(3, 2).

Let us check the length of the opposite sides of the quadrilateral that is formed by these points.

We have one pair of opposite sides equal.

Now, let us check the other pair of opposite sides.

The other pair of opposite sides is also equal. So, the quadrilateral formed by these four points is definitely a parallelogram.

Hence we have proved that the quadrilateral formed by the given four points is a .