Respuesta :
Answer:
Step-by-step explanation:
In the Cartesian coordinate system, the four quadrants are defined based on the signs of the x and y coordinates. The quadrants are as follows:
Quadrant I: Both x and y are positive.
Quadrant II: x is negative, y is positive.
Quadrant III: Both x and y are negative.
Quadrant IV: x is positive, y is negative.
Now, let's analyze each pair of points:
(p, q) and (q, p): These points could be in any quadrant, as there is no fixed relationship between the signs of p and q.
(p, q) and (2p, 2q): If (p, q) is in a particular quadrant, then (2p, 2q) will also be in the same quadrant because multiplying both coordinates by a positive constant does not change the quadrant.
(p, q) and (–p, –q): If (p, q) is in a particular quadrant, then (–p, –q) will be in the opposite quadrant because changing the sign of both coordinates flips the point across the origin.
(p, q) and (p – 2, q – 2): If (p, q) is in a particular quadrant, (p – 2, q – 2) may or may not be in the same quadrant. It depends on the specific values of p and q. If the subtraction does not change the signs of both coordinates, they will be in the same quadrant; otherwise, they may end up in different quadrants.
Therefore, the pair of points that must lie in the same quadrant is (2) (p, q) and (2p, 2q), as multiplying both coordinates by a positive constant does not change the quadrant.
