​​ What is the area of a rectangle with vertices at ​ (−4, 0) ​, ​ (−3, 1) ​ , (0, −2) , and (−1, −3) ?Enter your answer in the box. Do not round any side lengths.

Accepted Solution

Answer: [tex]6\ units^2[/tex]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: [tex]A=lw[/tex] 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: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] Knowing the coordinates of the vertices, you get: [tex]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[/tex] Therefore, substituting values into the formula [tex]A=lw[/tex], you get that the area of the rectangle is: [tex]A=(3\sqrt{2}\ units)(\sqrt{2}\ units)=6\ units^2[/tex]