Determine all possible quadrants in which the point can be located. Assume $x\ne 0$ and $y\ne 0$ . $(x,y),x+y<0$

A) Quadrants $\text{ II, III and IV }$
B) Quadrants II and III
C) Quadrants $\text{ I, II and IV }$
D) All quadrants
E) Quadrants I and II

Since $x+y<0$ , we know that the sum of the coordinates is negative, meaning the point is below the x-axis. Therefore, it cannot be in Quadrant I. Also, since $x<0$ , we know the point is to the left of the y-axis, so it cannot be in Quadrant IV. However, the point can be in either Quadrant II or III, since both have negative values for y. Therefore, the answer is A) Quadrants II, III, and IV.