Question

Explain and demonstrate (write words and show your work) how to find the area of the polygon. Side AB has endpoints at (-3, 6) and ( -1, 7). Side AB is one side of a rectangle that is not a square. Draw the other sides of the rectangle and Identify the other vertices as ordered pairs. Explain how you got the answer.

Answer 1

Given in the problem that the coordinates of the end points of a side of a rectangle is;

$A(-3,6),B(-1,7)$

Each of the angles of a rectangle is 90 degrees. Let a line BC be perpendicular to line AB.

The slope of line AB is;

$\begin{gathered} \text{Let;} \\ x_1=-3,y_1=6,x_2=-1,y_2=7 \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-6}{-1-(-3)} \\ m=\frac{1}{2} \end{gathered}$

When the two lines are perpendiculat to each other, the product of their slopes is negative one.

Hence, the slope of line BC is;

$\begin{gathered} m(\frac{1}{2})=-1 \\ m=-2 \end{gathered}$

Now, we can get the coordinate of point C (x,y). We have;

$\begin{gathered} B(-1,7),C(x_2,y_2),m=-2 \\ -2=\frac{y_2-7}{x_2-(-1)} \\ \text{Let;} \\ x_2=5 \\ -2=\frac{y_2-7}{6} \\ y_2=-12+7 \\ y_2=-5 \\ C(5,-5) \end{gathered}$$D(3,-6)$

This is a rectangle because the two sides are parallel to each other and opposite sides are equal in length.