Question

What is the area of the rectangle shown on the coordinate plane?

Answer 1

Answer:

26 square units.

Step-by-step explanation:

Consider rectangle with vertices A(-3,-1), B(1,5), C(4,3) and D(0,-3). The area of the rectangle is

$A=\text{length}\cdot \text{width}.$

Find the length and the width:

$AB=\sqrt{(-3-1)^2+(-1-5)^2}=\sqrt{16+36}=\sqrt{52},\\ \\BC=\sqrt{(4-1)^2+(3-5)^2}=\sqrt{9+4}=\sqrt{13}.$

Then the area of the rectangle ABCD is

$A_{ABCD}=AB\cdot BC=\sqrt{52}\cdot \sqrt{13}=\sqrt{4\cdot 13\cdot 13}=2\cdot 13=26\ un^2.$

Answer 2

The first thing you should do is draw the points given in the Cartesian plane. Once you have drawn the vertices (given points) of the rectangle, you must join them and draw the rectangle. Then you must find by the Pythagorean theorem two sides of the rectangle. Finally multiply both sides to find the area. I attach the solution.