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=(y_2-y_1)/(x_2-x_1) \\ m=(7-6)/(-1-(-3)) \\ m=(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((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=(y_2-7)/(x_2-(-1)) \\ \text{Let;} \\ x_2=5 \\ -2=(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.