Question

Name The Type Of Quadrilateral Formed By The Following Points -$(-3,5),(3,1),(0,3),(-1,-4)$ And Give Reasons For Your Answer

Answer 1

Step 1. Find the distance between the points using the distance formula.

Let the points are $A(-3,5),B(3,1),C(0,3),D(-1,-4)$

Know that the distance $\text{'}d\text{'}$ betwen the two points $\left(x_2-x_1\right)$and $\left(y_2-y_1\right)$is -

$d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Find the length of side AB:

$\begin{array}{c}AB=\sqrt{{\left(-3-3\right)}^2+{\left(5-1\right)}^2}\\ =\sqrt{-6^2+4^2}\\ =\sqrt{36+16}\\ =\sqrt{52}\end{array}$

Step 2 Find the length of side BC.

$\begin{array}{c}BC=\sqrt{{\left(3-0\right)}^2+{\left(1-3\right)}^2}\\ =\sqrt{3^2+{\left(-2\right)}^2}\\ =\sqrt{9+4}\\ =\sqrt{13}\end{array}$

Step 3 Find the length of the side CD.

$\begin{array}{c}CD=\sqrt{{\left(0+1\right)}^2+{\left(3+4\right)}^2}\\ =\sqrt{1^2+7^2}\\ =\sqrt{1+49}\\ =\sqrt{50}\end{array}$

Step 4. Find the length of side DA.

$\begin{array}{c}DA=\sqrt{{\left(-1+3\right)}^2+{\left(-4-5\right)}^2}\\ =\sqrt{2^2+9^2}\\ =\sqrt{4+81}\\ =\sqrt{85}\end{array}$

Since all sides of the quadrilateral are of different lengths.

Hence the quadrilateral formed by joining the points -$(-3,5),(3,1),(0,3),(-1,-4)$is not a special quadrilateral.