Question

find the area and perimeter of the rectangle with vertices $(1, -3)$, $(-2, -3)$, $(-2, 5)$, and $(1, 5)$.

Explanation:

Step1: Calculate the length and width

Use the distance formula for horizontal or vertical lines (since rectangle sides are horizontal/vertical).
For length (horizontal side): \(x_1 = 1,x_2=-2,y_1 = y_2=-3\). Length \(l=\vert1-(-2)\vert=\vert1 + 2\vert=3\).
For width (vertical side): \(x_1=-2,x_2=-2,y_1=-3,y_2 = 5\). Width \(w=\vert-3 - 5\vert=\vert-8\vert=8\).

Step2: Calculate the area

The formula for the area of a rectangle is \(A=l\times w\).
Substitute \(l = 3\) and \(w = 8\) into the formula: \(A=3\times8=24\).

Step3: Calculate the perimeter

The formula for the perimeter of a rectangle is \(P=2(l + w)\).
Substitute \(l = 3\) and \(w = 8\) into the formula: \(P=2(3 + 8)=2\times11 = 22\).

Answer:

The area is \(24\) and the perimeter is \(22\).