How to find magnitude from vectors?

Question

If $\vec B$ is added to $\vec A$, the result is 4.8i + 1.2j. If $\vec B$ is subtracted from $\vec A$ , the result is −3.20 + 5.8j. What is the magnitude of $\vec A$?

Am I supposed to subtract the two, so 8i - 4.6j? But then how would I find A's magnitude? To find magnitude, I would need to multiply direction, length, and a random choice of either sin or cos. BUt I can't do that with the data I have.

Answer 1

$$(A + B) + (A - B) = 2A$$ $$||2A|| = 2||A||$$

Edit: I missed the part about the magnitude. $$||A|| = \sqrt{A\cdot A}$$

Answer 2

Hint: Let $A=xi+yj$ and $B=ai+bj$. Then $$(x+a)i+(y+b)j=4.8i+1.2j$$ $$(x-a)i+(y-b)j=-3.2i+5.8j$$ Equating the compoenents (i.e. $x+a=4.8$, $y+b=1.2$ etc.) will give you four equations to solve for four variables.