Question

solve each problem.
1 a rectangle has vertices (-2,6),(6,6),(6, - 1), and (-2,-1). graph the rectangle in the coordinate plane. what is the area of the rectangle? what is the perimeter of the rectangle? show your work.

Explanation:

Step1: Find the length of the rectangle

The length of the rectangle is the distance between two points with the same y - coordinate. For points (-2,6) and (6,6), using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, since $y_1 = y_2 = 6$, the length $l=\vert6-(-2)\vert=8$.

Step2: Find the width of the rectangle

The width of the rectangle is the distance between two points with the same x - coordinate. For points (6,6) and (6, - 1), since $x_1=x_2 = 6$, the width $w=\vert6-(-1)\vert=7$.

Step3: Calculate the area of the rectangle

The area formula of a rectangle is $A=l\times w$. Substituting $l = 8$ and $w = 7$, we get $A=8\times7 = 56$.

Step4: Calculate the perimeter of the rectangle

The perimeter formula of a rectangle is $P=2(l + w)$. Substituting $l = 8$ and $w = 7$, we get $P=2(8 + 7)=2\times15 = 30$.

Answer:

The area of the rectangle is 56 square units and the perimeter is 30 units.