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

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2 Answers

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