Answer:
(c) The set of all points in quadrants II and IV (x and y have opposite signs).
(d) The set of all points on the x-axis or y-axis.
Step-by-step explanation:
The Cartesian plane is divided into four quadrants.
Quadrant I is where x and y are positive, and the rest of the quadrants follow in a counterclockwise direction.
- Quadrant I: x > 0 and y > 0 → (x, y)
- Quadrant II: x < 0 and y > 0 → (-x, y)
- Quadrant III: x < 0 and y < 0 → (-x, -y)
- Quadrant IV: x > 0 and y < 0 → (x, -y)
Part (c)
Given condition: xy < 0
For the given condition, x should be positive and y should be negative, or x should be negative and y should be positive, i.e. x and y should have opposite signs.
- x is negative and y is positive in quadrant II.
- x is positive and y is in negative quadrant IV.
Therefore, the description that satisfies the given condition is:
- The set of all points in quadrants II and IV (x and y have opposite signs).
Part (d)
Given condition: xy = 0
For the given condition, x should be zero, or y should be zero, or x and y should both be zero.
- x is zero for all points on the y-axis.
- y is zero for all points on the x-axis.
- x and y are both zero at the origin, which is on both axes.
Therefore, the description that satisfies the given condition is:
- The set of all points on the x-axis or y-axis.
