Question

2.) given a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4), graph the points on the coordinate plane provide. what is the perimeter of the polygon?

Explanation:

Step1: Determine the lengths of the sides

• For the horizontal side between \((-3,1)\) and \((5,1)\):

Using the distance formula for horizontal points (\(y\)-coordinates are the same), \(d=\vert x_2 - x_1\vert\). Here \(x_1=-3,x_2 = 5\), so \(d=\vert5-(-3)\vert=\vert5 + 3\vert=8\).

• For the vertical side between \((-3,1)\) and \((-3,4)\):

Using the distance formula for vertical points (\(x\)-coordinates are the same), \(d=\vert y_2 - y_1\vert\). Here \(y_1 = 1,y_2=4\), so \(d=\vert4 - 1\vert=3\).

• The other two sides (opposite sides of a rectangle) have the same lengths as the first - two sides (since it's a rectangle, opposite sides are equal).

Step2: Calculate the perimeter

The perimeter \(P\) of a rectangle is given by \(P=2(l + w)\), where \(l = 8\) (length) and \(w = 3\) (width).
\(P=2(8 + 3)=2\times11 = 22\).

Answer:

\(22\)