Answer:
A (-1;10)
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:
\(m_{AC}=(\frac{x+5}{2};\frac{y+4}{2} )\)
However we know the exact coordinates of the middle point, which are (2,7), that means:
\(\frac{x+5}{2}=2\\ x=4-5=-1\)
\(\frac{y+4}{2}=7\\ y=14-4=10\)
Therefore, the coordinates of A are (-1;10)
