#### 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.

#### Solution

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.

Is there an error in this question or solution?

Solution Find the Type of the Quadrilateral If Points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) Are Joined Serially. Concept: Slope of a Line.