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

$LetA(-2,-1)B(4,0),C(3,3)andD(-3,2)\text{be the given points.}\text{Now, slope of}AB=\frac{0+1}{4+2}=\frac{1}{6}\text{Slope of}BC=\frac{3-0}{3-4}=-3\text{Slope of}CD=\frac{2-3}{-3-3}=\frac{1}{6}\text{Slope of}DA=\frac{-1-2}{-2+3}=-3\text{Clearly, we have,}\text{Slope of AB = Slope of CD}\text{Slope of BC = Slope of DA}\text{As the slopes of opposite sides are equal.}\text{Therefore, both pair of opposite sides are parallel.}\text{Hence, the given points are the vertices of a parallelogram.}$