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

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) (Show Source): You can put this solution on YOUR website!
For part a:

Use the slope formula, , 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
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:

Use the midpoint formula, (,) 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.
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.

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