The coordinates of an ordered pair have opposite signs. In which quadrant(s) must the ordered pair lie?
The ordered pair must lie in either the second or fourth quadrant.
An ordered pair with opposite signs for its coordinates will lie in either Quadrant II or Quadrant IV of the Cartesian plane.
To determine in which quadrant(s) an ordered pair must lie when the coordinates have opposite signs, we need to understand the signs of the coordinates in each quadrant. Here's a step-by-step explanation of how to solve this:
1. Recall the four quadrants on a coordinate plane:
- Quadrant I: Positive x, Positive y
- Quadrant II: Negative x, Positive y
- Quadrant III: Negative x, Negative y
- Quadrant IV: Positive x, Negative y
2. If an ordered pair has opposite signs, it means that one of the coordinates is positive, and the other is negative.
3. Consider the possibilities:
- If the x-coordinate is positive and the y-coordinate is negative, the ordered pair lies in Quadrant IV.
- If the x-coordinate is negative and the y-coordinate is positive, the ordered pair lies in Quadrant II.
Therefore, if an ordered pair has opposite signs, it must lie in Quadrant II or Quadrant IV, depending on which coordinate is positive and which is negative.