Question

Given parallelogram ABCD with C(5,4), find the coordinates of A if the diagonals AC and BD intersect at (2,7).

Answer 1

Plot graph and count for A. 

A (-1,10)

Answer 2

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)