Vertices of a Parallelogram. Can anyone please help me???

Question

1. A parallelogram has the vertices (0, 3), (3, 0), (0, -3) and (-3, 0).  Determine what type of parallelogram.Find the perimeter and area and then graph.

2.  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.

Can anyone please help me with these two questions?? I am having a hard time understanding this assignment..

Answer 1

(1)

Step 1:

The vertices of a parallelogram are , , and .

The sides of the parallelogram are and .

Find the length of the sides of the parallelogram.

Distance between the two points and is .

Distance .

Distance .

Distance .

Distance .

Distance .

Distance .

Distance .

Distance .

Step 2:

The diagonals of the parallelogram are and .

Find the diagonals of the parallelogram.

The length of the diagonal .

.

The length of the diagonal .

.

Step 3:

The four sides of the parallelogram has equal lengths and the lengths of the diagonals are equal.

Therefore, the parallelogram is a square.

The side of the square is .

Perimeter of the square is .

.

Area of the square is .

.

Comments

Contd . . .

Step 4:

Graph:

Draw the coordinate plane.

Plot the vertices , , and .

Draw the line segments , and .

Solution:

The parallelogram is a square.

The perimeter is .

The area is .

Graph:

.

Answer 2

(2)

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 between the two points  and  is .

Distance .

Distance between the two points  and  is .

Distance .

Since the sides are of equal length, the parallelogram can be a rhombus or a square.

Step 2:

Find the distance between the opposite vertices.

Distance .

Distance .

Distance .

Distance .

Since the four sides of the parallelogram are equal and the length of the diagonals 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 .

Comments

Contd...

Step 4:

Graph:

Draw the coordinate plane.

Plot the vertices  and .

Draw the line segments ,  and .

Solution:

The parallelogram  is a Rhombus.

The perimeter of the rhombus is  units.

The area of the rhombus is 21 sq-units.

Graph of the rhombus is

.