Given parallelogram abcd with c(5,4), find the coordinates of a if the diagonals ac and bd intersect at (2,7).

Step-by-step explanation:

From the problem, we deduct that point (2,7) is a middle point for diagonals AC and BD, because the intersection of diagonals in a parallelogram intercept in the middle point of each one.

So, the coordinates of A are (x,y) unknown, and coordinates of C are (5,4), applying the definition of middle point:

However we know the exact coordinates of the middle point, which are (2,7), that means:

Therefore, the coordinates of A are (-1;10)