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

A (-1;10)

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)=((x+5)/(2);(y+4)/(2) )`

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

`(x+5)/(2)=2\\ x=4-5=-1`

`(y+4)/(2)=7\\ y=14-4=10`

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

Answer 2

Plot graph and count for A.

A (-1,10)