SOLUTION: It is given that PQRS is a parallelogram. Graph PQRS. Decide whether its a rectangle, a rhombus , a square or none of the above #1) P(-6,5), Q(4,11) R(7,7) S(-3,1) #2)

Algebra ->  Parallelograms -> SOLUTION: It is given that PQRS is a parallelogram. Graph PQRS. Decide whether its a rectangle, a rhombus , a square or none of the above #1) P(-6,5), Q(4,11) R(7,7) S(-3,1) #2)       Log On


   

Question 807738: It is given that PQRS is a parallelogram. Graph PQRS. Decide whether its a rectangle, a rhombus , a square or none of the above
#1) P(-6,5), Q(4,11) R(7,7) S(-3,1)
#2) P(-7,-2), Q(-2,-2), R(-2,-7) S(-7,-7) help asap
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
#1) P(-6,5), Q(4,11) R(7,7) S(-3,1)
This quadrilateral looks like a rectangle, but it is not.
The angles are not 90%5Eo .
Perpendicular lines/segments have slopes whose product is -1 .
Slope of PQ =%2811-5%29%2F%284-%28-6%29%29=6%2F10=3%2F5
Slope of QR =%287-11%29%2F%287-4%29=%28-4%29%2F3=-4%2F3
The product of the slopes is %283%2F5%29%2A%28-4%2F3%29=-4%2F5%3C%3E-1 ,
so PQ and QR are not perpendicular, and PQRS is neither a square nor a rectangle.
Since obviously PQ is much longer than QR, it is not a rhombus either.

#2) P(-7,-2), Q(-2,-2), R(-2,-7) S(-7,-7)
This one is obviously a square of side length 5. The sides are the same length and perpendicular to each other because they are parallel to the x- and y-axes.