Solving a Vector Problem in the xy Plane

[jpodo]

Here is the problem I can't solve:

You are given a vector in the xy plane that has a magnitude of 80.0 units and a y component of -60.0 units.

(a) What are the two possibilities for its x component?

(b) Assuming the x component is known to be positive, specify the vector which, if you add it to the original one would give a resultant vector that is 70.0 units long and points entirely in the -x direction. (looking for Magnitude + Direction)

 

[genneth]

Suppose that a vector has the components x and y, and a magnitude r. What's the equation that links x, y and r?