Question

A figure drawn in the coordinate plane has the coordinates J(‒1,5), K(6,5), L(9,1) and M(2,1).

1) Use what you have learned in this unit to prove that the figure is either a parallelogram, rectangle, square or a rhombus.
2) Use what you have learned in this lesson to find the area and perimeter of the figure.

Answer 1

It's important that you actually plot the 4 given points and draw the polygon. I've done that and have seen right away that the polygon is not a square or rectangle. It does, however, have 2 sets of parallel sides, which means that it's a parallelogram.

The 2 horiz. lines in this figure are y=1 and y=5. The distance between these two y-values is the "width" of the parallelogram: width=4.
The 2 slanted lines have what length? Hint: What is 9-2? What is 6-(-1)?

The area of this parallelogram is = to the product of the width (4) and the length (7).

How do you find the length of the slanted end lines? You must know this fact to find the perimeter of this parallelogram.

Answer 2

It is a parallelogram.
We can easily count the dimensions from the x and y values.
From the Pythagorean Theorem, we can calculate the sides equaling 5 and the top and bottom each measure 7.
The perimeter = 5 * 2 + 7 * 2 = 24
area = height * top (or bottom) length
area = 4 * 7 = 28