Question

By using the concept of slope, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.

Answer 1

Let A (−2, −1), B (4, 0), C (3, 3) and D (−3, 2) be the given points.

Now, slope of AB$=\frac{0+1}{4+2}=\frac{1}{6}$

Slope of BC$=\frac{3-0}{3-4}=-3$

Slope of CD$=\frac{2-3}{-3-3}=\frac{1}{6}$

Slope of DA$=\frac{-1-2}{-2+3}=-3$

Clearly, we have,
Slope of AB = Slope of CD
Slope of BC = Slope of DA

As the slopes of opposite sides are equal,
Therefore, both pair of opposite sides are parallel.
Hence, the given points are the vertices of a parallelogram.