We can tell that the slopes of the opposite sides of our quadrilateral are equal. Therefore, both pairs of opposite sides are parallel and the quadrilateral is a parallelogram. We can also tell that the consecutive sides are perpendicular, as their slopes are opposite reciprocals.
2 ( - 1/2 ) = -1
Therefore, our quadrilateral is either a rectangle or a square. To check, we can find the lengths of its sides using the Distance Formula.
Side
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Simplify
JK
J( 1,-3), K( 3,1)
sqrt(( 3- 1)^2+( 1-( -3))^2)
sqrt(20)
KL
K( 3,1), L( 7, -1)
sqrt(( 7- 3)^2+( -1- 1)^2)
sqrt(20)
LM
L( 7, -1), M( 5, -5)
sqrt(( 5- 7)^2+( -5-( -1))^2)
sqrt(20)
MJ
M( 5, -5), J( 1,-3)
sqrt(( 1- 5)^2+( -3-( -5))^2)
sqrt(20)
Our parallelogram has four congruent sides. Therefore, the most precise name for this quadrilateral is a square.
Area
To find the area, we can use the formula for the area of a square.
A=s^2
In this case s= sqrt(20). Let's substitute it in the formula to find A.
A= ( sqrt(20))^2 ⇔ A=20
The area of our square is 20 units squared.
