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

Question

I'm guessing the shape is a square because a square has all equal sides, yet I am not sure, please help??

Answer 1

You can start off this problem by doing a sketch of the parallelogram, just to have a visual representation.

 

Secondly, since you need to find the perimeter and area of the parallelogram, that requires knowing the lengths of the sides. Use the distance formula for all sides.

 

√ = square root, x₁ = 1st x- coordinate, x₂ = 2nd x-coordinate, y₁=1st y- coordinate, and y₂ = 2nd y-coordinate

 

all values are under the square root sign

√(x₂-x₁)² + (y₂-y₁)² = distance formula

 

so I assigned letters to each coordinate: A(0,3), B(3, 0), C(0, -3) and D(-3, 0)

 

AB: √(3 - 0)² + (0 - 3)² = √(3)² + (-3)² = √(9) + (9) = √18

BC: √(0 - 3)² +(-3 - 0)² = √(-3)² +(-3)² =√(9) + ( 9) = √18

CD: √(-3 - 0)² +(0 - -3)² = √(-3)² +(3)² = √(9) + (9) = √18

AD: √(-3 - 0)² +(0 - 3)² = √(-3)² +(-3)² =√(9) + (9) = √18

 

Since all sides are congruent,therefore Its a square.

 

Area = s² = √18² = 18

Perimeter = add all sides: 4(√18)= 4√18, but in simplest radical form its: 4• √9 •√2 = 4 • 3 •√2 = 12√2

Answer 2

It's a square. Area is 18 and perimeter 12√2.

 

 

Answer 3

Wrong. See Ralph's answer!

 

It is indeed a 3 x 3 square, with perimiter = 12 and area = 9. Not sure what type of proof may be needed though.