Question

Say true or false.

Points $(1,7),(4,2),(-1,-1)$ and $(-4,4)$ are the vertices of a square.

• A. True
• B. False

Answer 1

The correct option is A True

Let $A(1,7),B(4,2),C(-1,-1)$ and $D(-4,4)$ be the given co-ordinates.

1. Diagonals $BD$ and $AC$

BD $=\sqrt{(4+4{)}^2+(2-4{)}^2}=\sqrt{68}$

AC $=\sqrt{(1+1{)}^2+(7+1{)}^2}=\sqrt{68}$

$\therefore AC=BD$

$\therefore$ the diagonals are equal.

2. Sides $AB,BC,CD$ and $DA$

Length $AB=\sqrt{{\left(41\right)}^2+{\left(27\right)}^2}=\sqrt{34}$

Length $BC=\sqrt{{\left(14\right)}^2+{\left(12\right)}^2}=\sqrt{34}$

Length $CD=\sqrt{{\left(41\right)}^2+{\left(41\right)}^2}=\sqrt{34}$

Length $DA=\sqrt{{\left(41\right)}^2+{\left(47\right)}^2}=\sqrt{34}$

Therefore, $\square ABCD$ is a square since sides $AB,BC,CD$ and $DA$ are equal and the diagonals are also equal.