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39 votes
The figure shows parallelogram PQRS on a coordinate plane. Diagonals SQ and PR intersect at point T.What are the coordinates of point Q in terms of a, b, and c.

The figure shows parallelogram PQRS on a coordinate plane. Diagonals SQ and PR intersect-example-1
User Rodrigo Borba
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3.4k points

1 Answer

20 votes
20 votes

From the figure, we know that segments PQ and SR have the same lenght and they are parallel. This implies that the y-coordinate of Q is


Q=(x\text{ , 4b)}\ldots(A)

Now, in order to find the x-coordinate of Q, we must use the fact that


PQ=SR

this implies that


PQ=x-4c=SR=4a

Therefore, x is given by


\begin{gathered} x-4c=4a \\ x\questeq4a+4c\ldots(B) \end{gathered}

Then, from equations A and B, the point Q is given by


Q=(4a+4c,4b)

The figure shows parallelogram PQRS on a coordinate plane. Diagonals SQ and PR intersect-example-1
User Nathanjosiah
by
3.2k points
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