Question

draw a polygon with vertices at ( a(-1,6) ), ( b(-7,6) ), ( c(-7,-3) ), and ( d(-1,-3) ). then find the perimeter of the polygon.
use structure how can you use the coordinate plane to draw the polygon and find its perimeter?

Explanation:

Step1: Determine the type of polygon

Since the \(y -\)coordinates of \(A(-1,6)\) and \(B(-7,6)\) are the same, \(AB\) is a horizontal line.
The distance formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\vert x_2 - x_1\vert\) for horizontal lines (\(y_1 = y_2\)) and \(d=\vert y_2 - y_1\vert\) for vertical lines (\(x_1=x_2\)).
For \(AB\): \(x_1=-1,x_2 = - 7,y_1=y_2 = 6\), so \(AB=\vert-7-(-1)\vert=\vert-7 + 1\vert=6\).
For \(BC\): \(x_1=-7,y_1 = 6,x_2=-7,y_2=-3\), so \(BC=\vert-3 - 6\vert=9\).
For \(CD\): \(x_1=-7,y_1=-3,x_2=-1,y_2=-3\), so \(CD=\vert-1-(-7)\vert=6\).
For \(DA\): \(x_1=-1,y_1=-3,x_2=-1,y_2 = 6\), so \(DA=\vert6-(-3)\vert=9\).

Step2: Calculate the perimeter

The perimeter \(P\) of a polygon is the sum of the lengths of its sides.
\(P=AB + BC+CD + DA\)
Substitute \(AB = 6\), \(BC = 9\), \(CD = 6\), \(DA = 9\) into the formula:
\(P=6 + 9+6 + 9\)
\(P=(6 + 6)+(9 + 9)\)
\(P = 12+18\)
\(P=30\)

Answer:

The perimeter of the polygon is \(30\).