Question

What is the area of a rectangle with vertices at ​ (−4, 0) ​, ​ (−3, 1) ​ , (0, −2) , and (−1, −3) ?

Answer 1

Answer: $6\ units^2$

Step-by-step explanation:

Plot the vertices of the rectangle on a coordinate plane (Observe the figure attached where the rectangle is identified as ABCD).

The area of a rectangle can be calculated with this formula:

$A=lw$

Where "l" is the lenght and "w" is the width.

In order to find the lenght and the width, you can use the formula for calculate the distance between two points:

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

Knowing the coordinates of the vertices, you get:

$w=d_{AB}=\sqrt{(-4-(-3))^2+(0-1)^2}=\sqrt{2}\ units\\\\l=d_{BC}=\sqrt{(0-(-3))^2+(-2-1)^2}=3\sqrt{2}\ units$

Therefore, substituting values into the formula $A=lw$, you get that the area of the rectangle is:

$A=(3\sqrt{2}\ units)(\sqrt{2}\ units)=6\ units^2$