A parallelogram has the vertices (-1, 2), (4, 4), (2, -1) and (-3, -3).  Determine what type of parallelogram.  Find the perimeter and area and graph.

Step 1:

The vertices of the parallelogram are and .

Find the distance between each and every points.

The sides of the parallelogram are and .

The diagonals of the parallelogram are and .

Distance between the two points and is .

Distance between the two points and is .

Distance .

Distance between the two points and  is .

Distance .

Distance .

Distance .

Distance between the two points and is .

Distance .

Since the distances are equal, the parallelogram can be a rhombus or a square.

Step 2:

Find the distance between the opposite sides.

Distance .

Distance .

Distance .

Distance .

Since the four sides of the parallelogram are equal and the lengths of the diagonal are not equal, the parallelogram is a Rhombus with side units.

Step 3:

Side of the rhombus is .

Perimeter of a rhombus: , where is side of the rhombus.

units.

Area of a rhombus: , where and are the diagonals of the rhombus.

Substitute and .

Step 4:

Draw the coordinate plane.

Plot the vertices and .

Draw the line segments , and .

Solution:

The parallelogram are is a Rhombus.

The perimeterof the rhombus is units.

The area of the rhombus is sq-units.

Graph of the rhombus is

.

.