Chapter 6.5, Problem 6CYU

To determine

To determine if the given vertices are of a rhombus, a rectangle or a square.

Answer to Problem 6CYU

It is a rectangle.

Explanation of Solution

Given information :

First we shall find the distance of all the sides.

  $\begin{array}{l}QR=\sqrt{{\left(2-\left(-1\right)\right)}^2+{\left(-1-\left(-2\right)\right)}^2}=\sqrt{10}\\ RS=\sqrt{{\left(1-2\right)}^2+{\left(4-\left(-1\right)\right)}^2}=\sqrt{26}\\ ST=\sqrt{{\left(-2-1\right)}^2+{\left(3-4\right)}^2}=\sqrt{10}\\ TQ=\sqrt{{\left(-2-\left(-1\right)\right)}^2+{\left(3-\left(-2\right)\right)}^2}=\sqrt{26}\end{array}$

As opposite sides are equal, hence it is a rectangle.