Question 281405: Points P(1,2), Q(-1,-1), R(1,-3) are given: determine the coordinates or point S for PQRSto be a parallelogram
Answer by subudear(62)   (Show Source):
You can put this solution on YOUR website! For a parallelogram PQRS you can consider either PQ and RS lines or PS and QR
Lets take PQ ans RS line. Let coordinate for S be (x,y)
Then slope for PQ and RS should be same.
Slope of PQ line = (-1 - 2)/(-1 - 1) = 3/2
Slope of RS line = (y - -3)/(x - 1) = (y+3)/(x - 1)
equating both of them
(y+3)/(x - 1) = 3/2
2(y+3) = 3(x-1)
2y -3x = -9
Now Lets take PS and QR line. Let coordinate for S be (x,y)
Then slope for PS and QR should be same.
Slope of PS line = (y - 2)/(x - 1)
Slope of QR line = (-3 - -1)/(1 - -1) = -1
equating both of them
(y-2)/(x - 1) = -1
(y-2) = -(x-1)
y +x = 3
solving the above 2 equations we get
x = 3, y = 0
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