SOLUTION: Place three vertices of a parallelogram ABCD at A(0, 0), B(2a, 2b) and D (2c, 2d). Use gradients to show that C = (2a + 2c, 2b + 2d) completes the parallelogram

Question 1177056: Place three vertices of a parallelogram ABCD at A(0, 0), B(2a, 2b)
and D (2c, 2d).
Use gradients to show that C = (2a + 2c, 2b + 2d) completes the
parallelogram
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
slope of line = (y2-y1)/(x2-x1) where )x1,y1) and (x2,y2) are the two points on the line
Slope of AB = (2b-0)/(2a-0)= 2b/2a=b/a
slope of CD = b/a ( parallel to AB)
slope of line = (y2-y1)/(x2-x1) where )x1,y1) and (x2,y2) are the two points on the line
slope of CD = ((2b+2d)-2d) /( (2a+2c)-2c) = b/a

Therefore C = (2a + 2c, 2b + 2d) completes the
parallelogram

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