What is the area of the parallelogram?

Question

it's on a coordinate plane. these are the points (-4,1), (7,2), (5,-3), (-6,-3)

Answer 1

What is the area of the parallelogram?
it's on a coordinate plane. these are the points (-4,1), (7,2), (5,-3), (-6,-3)

 

Solution:

 

The point (-4,1) is in the 2nd quadrant

The point (7,2) is in the 1st quadrant

The point (5,-3) is in the 4th quadrant

The point (-5,-3) is in the 3rd quadrant

 

By inspection this is not a parallelogram. the coordinate of the point in the 1st quadrant must be 1, and the point should be (7,1) rather than (7,2)

 

if you plot the points on a Cartesian system of coordinates graph, you get a parallelogram. To find its area you need the length and height

 

the length is the distance between points (-4,1) and (7,1) or between the points (-6,-3) and ( 5,-3)

 

The height is the distance between points ( 7,1) and (5,-3) or points

(-4,1) and (-6,-3)

 

L = √(7+4)²+(1-1)²=√11²+1²=√121+1=√121=11

 

or L=√(-3+3)²+(5+6)² = √0²+11²=√121=11

 

H= √(-3-1)²+(5-7)²=√(-4)²+(-2)²=√16+4=√20

 

or H= √(-3-1)²+(-6+4)²=√(-4)²+(-2)²=√16+4=√20

 

the area of the parallelogram is A = LH= 11√20 = square units