Question

if point q does not lie on the x - axis or the y - axis and its x and y coordinates have opposite signs, then point q must be located in which of the 4 quadrants, as shown below?
a. i only
b. iii only
c i or iii only
d. i or iv only
e ii or iv only

Explanation:

Step1: Analyze quadrant I

In quadrant I, \(x>0\) and \(y > 0\). The signs of \(x\) and \(y\) are the same.

Step2: Analyze quadrant II

In quadrant II, \(x<0\) and \(y>0\). The signs of \(x\) and \(y\) are opposite.

Step3: Analyze quadrant III

In quadrant III, \(x < 0\) and \(y<0\). The signs of \(x\) and \(y\) are the same.

Step4: Analyze quadrant IV

In quadrant IV, \(x>0\) and \(y < 0\). The signs of \(x\) and \(y\) are opposite.

Answer:

E. II or IV only