Respuesta :

Plot graph and count for A. 

A (-1,10)

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:

[tex]m_{AC}=(\frac{x+5}{2};\frac{y+4}{2} )[/tex]

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

[tex]\frac{x+5}{2}=2\\ x=4-5=-1[/tex]

[tex]\frac{y+4}{2}=7\\ y=14-4=10[/tex]

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

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