SOLUTION: Given: Quadrilateral PQRS P= (-10,7), Q=(4,3), R=(-2,-5), S=(-16,1) a.Prove taht the quadrilateral PQRS is not a parallelogram b. Prove that the quadrilateral formed by joining

Algebra ->  Parallelograms -> SOLUTION: Given: Quadrilateral PQRS P= (-10,7), Q=(4,3), R=(-2,-5), S=(-16,1) a.Prove taht the quadrilateral PQRS is not a parallelogram b. Prove that the quadrilateral formed by joining       Log On


   

Question 818113: Given: Quadrilateral PQRS
P= (-10,7), Q=(4,3), R=(-2,-5), S=(-16,1)
a.Prove taht the quadrilateral PQRS is not a parallelogram
b. Prove that the quadrilateral formed by joining consecutive midpoints of the sides of PQRS is a parallelogram
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
For part a:
  1. Use the slope formula, m+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29, to find four slopes:
    • Slope of the line through P and Q
    • Slope of the line through Q and R
    • Slope of the line through R and S
    • Slope of the line through S and P
  2. If the slope through P and Q equals the slope through R and S and the slope through Q and R equals the slope through S and P, then PQRS is a parallelogram. If not, then PQRS is not a parallelogram.
For part b:
  1. Use the midpoint formula, (%28x%5B1%5D%2Bx%5B2%5D%29%2F2,%28y%5B1%5D%2By%5B2%5D%29%2F2) to find four midpoints:
    • The midpoint between P and Q. Name this point A.
    • The midpoint between Q and R. Name this point B.
    • The midpoint between R and S. Name this point C.
    • The midpoint between S and P. Name this point C.
  2. Perform the same steps on ABCD as you did on PQRS in part a: Find four slopes and see if you end up with two pairs of equal slopes. If so, then ABCD is a parallelogram. If not, ABCD is not a parallelogram.