Question

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.

Answer 1

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

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