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,
Slope of AB = $\frac{-7+2}{-3+4}=-5$
Slope of BC = $\frac{-2+7}{3+3}=\frac{5}{6}$
Slope of CD = $\frac{3+2}{2-3}=-5$
Slope of AD = $\frac{3+2}{2+4}=\frac{5}{6}$
Opposite sides are parallel.
AC = $\sqrt{{\left(3+4\right)}^2+{\left(-2+2\right)}^2}=\sqrt{49}=7$
BD = $\sqrt{{\left(3+7\right)}^2+{\left(2+3\right)}^2}=\sqrt{125}=5\sqrt{5}$
Diagonals are not equal.
Hence, the given points form a parallelogram.