document.write( "Question 818113: Given: Quadrilateral PQRS
\n" ); document.write( "P= (-10,7), Q=(4,3), R=(-2,-5), S=(-16,1)
\n" ); document.write( "a.Prove taht the quadrilateral PQRS is not a parallelogram
\n" ); document.write( "b. Prove that the quadrilateral formed by joining consecutive midpoints of the sides of PQRS is a parallelogram \n" ); document.write( "
Algebra.Com's Answer #492408 by jsmallt9(3758)\"\" \"About 
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.
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