Question

On a coordinate plane, the vertices of a rectangle are (–1, 1), (3, 1), (–1, –4), and (3, –4). What is the perimeter of the rectangle?

Answer 1

Given that,

The vertices of a rectangle are (–1, 1), (3, 1), (–1, –4), and (3, –4).

To find,

The perimeter of the rectangle.

Solution,

Let the points are :

A(–1, 1), B(3, 1), C(3, –4) and D(–1, –4)

Let's find AB and BC using distance formula :

$AB=\sqrt{(3-(-1))^2+(1-1)^2} \\\\=4\ \text{units}$

$BC=\sqrt{(3-3)^2+(-4-1)^2} \\\\=5\ \text{units}$

The perimeter of a rectangle = 2(sum of two adjacent sides)

= 2(AB+BC)

= 2(4+5)

= 18 units

So, the perimeter of the rectangle is 18 units.