Question

Find the type of the quadrilateral if points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) are joined serially.

Answer 1

The given points are A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3).
If they are joined serially so, 

\[\text{Slope of AB} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

= \[\frac{-7 - (-2)}{-3 - (-4)}\]

= \[\frac{- 7 + 2}{- 3 + 4} = - 5\]

\[\text{Slope of BC} = \frac{y_2-y_1}{x_2-x_1}\]

= \[\frac{-2-(-7)}{3-(-3)}\]

=  \[\frac{- 2 + 7}{3 + 3} = \frac{5}{6}\]

\[\text{Slope of CD} = \frac{y_2-y_1}{x_2-x_1}\]

= \[\frac{3-(-2)}{2-3}\]

= \[\frac{3 + 2}{2 - 3} = - 5\]

\[\text{Slope of AD} = \frac{y_2-y_1}{x_2-x_1}\]

= \[\frac{3-(-2)}{2-(-4)}\]

= \[\frac{3 + 2}{2 + 4} = \frac{5}{6}\]

Slope of AB = slope of CD

∴ line AB || line CD

Slope of BC = slope of AD

∴ line BC || line AD

Both the pairs of opposite sides of ∆ABCD are parallel.

∴ ABCD is a parallelogram.

∴ The quadrilateral formed by joining the points A, B, C and D is a parallelogram.