5. If \( x>0, y<0 \) then \( (-x,-y) \) lies in

Ah, the fascinating world of coordinate geometry! When \( x > 0 \) (which means \( -x < 0 \)) and \( y < 0 \) (which means \( -y > 0 \)), the point \( (-x, -y) \) transforms the signs and places our point in the second quadrant of the Cartesian plane. That's the area where x is negative and y is positive! Isn’t it amazing how signs can change the entire location of a point? Thinking of practical applications, this concept helps us understand various fields such as physics and engineering, where coordinates dictate positions in a given space. For instance, if you're plotting forces or movements in opposite directions, knowing how to manipulate these coordinates is crucial. So next time you're drawing out a scenario, remember how that simple sign change can lead to entirely different quadrants and implications!