Question

b. Shirley was given the following points and asked to calculate the area, but her graph paper is not big enough. Calculate the area of Shirley's rectangle, and explain to her how she can determine the area without graphing the points. Shirley's points (352, 150), (352, 175), (456, 150), and (456, 175)

Answer 1

The given points are

(352, 150)

(352, 175)

(456, 150)

(456, 175)

Each point represents one vertex of the rectangle.

The points that have the same x-coordinate are in the same vertical line, this means that the diference between the y-coordinates of the point determine the length of the width of the rectangle.

Since is a rectangle both vertical sides are equal.

Using the points

(352, 150)

(352, 175)

You can calculate the width as:

`\begin{gathered} w=y_2-y_1 \\ w=175-150 \\ w=25\text{units} \end{gathered}`

The points that have the same y-coordinate are in the same horizontal line, if you calculate the difference between the x-coordinates of said points, you can determine the length of the rectangle.

Using the points

(456, 150)

(352, 150)

You can calculate the length as

`\begin{gathered} l=x_2-x_1 \\ l=456-352 \\ l=104\text{units} \end{gathered}`

So the rectangle has a length of 104 and a width of 25. Using these values you can calculate the area:

`\begin{gathered} A=wl \\ A=25\cdot104 \\ A=2600\text{units}^2 \end{gathered}`