Determining Quadrants

Question

if -x>0 and y<0, then (-x,y) is in which quadrant(s)?

Answer 1

I like to try and plug numbers into to see what happens.

Lets try x=2, which would mean -2>0 which obviously ins't true because all negative numbers are less than zero.

If we try x=-2, -(-2)>0 -> 2>0 which is True.

So we need to have negative numbers for x. What about y?

If y=3 then our expression is 3<0 which is not correct.

y=-3 does work as -3<0.

So we need our x values to be negative and our y values to be negative.

Quadrant I is for positive x and y, quadrant II for negative x, positive y, quadrant III for negative x and y, and quadrant IV for postive x, negative y. Based on this it would appear the region you're interested in is quadrant III and no other quadrant as your x and y values both need to be negative.

Answer 2

-x > 0, then -x in ether QI or QIV.

y < 0, then y in either QIII or QIV

In which quadrant could (-x, y) be?