Question

rectangle abcd is graphed in the coordinate plane. the following are the vertices of the rectangle: a(-2,1), b(3,1), c(3,4), and d(-2,4). what is the perimeter of rectangle abcd? units

Explanation:

Step1: Calculate the length of side \(AB\)

For points \(A(-2,1)\) and \(B(3,1)\), since the \(y\)-coordinates are the same, use the distance formula for horizontal distance \(d = |x_2 - x_1|\).
\(AB=|3-(-2)|=|3 + 2|=5\)

Step2: Calculate the length of side \(BC\)

For points \(B(3,1)\) and \(C(3,4)\), since the \(x\)-coordinates are the same, use the distance formula for vertical distance \(d=|y_2 - y_1|\).
\(BC = |4 - 1|=3\)

Step3: Use the perimeter formula of a rectangle

The perimeter formula of a rectangle is \(P=2(l + w)\), where \(l\) is the length and \(w\) is the width. Here \(l = 5\) (length of \(AB\)) and \(w = 3\) (length of \(BC\)).
\(P=2(5 + 3)=2\times8 = 16\)

Answer:

\(16\)