The coordinates of an ordered pair her opposite signs. In which quadrant is the ordered pair lie? Explain.
If the coordinates of an ordered pair have opposite signs, it means that one coordinate is positive and the other is negative.
In the first quadrant, both coordinates are positive.
In the second quadrant, the x-coordinate is negative and the y-coordinate is positive.
In the third quadrant, both coordinates are negative.
In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative.
Therefore, the ordered pair with opposite signs will lie in either the second or fourth quadrant. This is because one coordinate has to be positive (in the first or fourth quadrant), and the other coordinate has to be negative (in the second or third quadrant).
To determine in which quadrant an ordered pair with opposite sign coordinates lies, we can refer to the signs of the x- and y-coordinates. Here's how you can figure it out:
1. Take a look at the x-coordinate (the first value in the ordered pair). If it is positive and the y-coordinate is negative, or if the x-coordinate is negative and the y-coordinate is positive, then the ordered pair has opposite sign coordinates.
2. Now, think about the four quadrants on a cartesian plane:
- Quadrant I: Both x and y coordinates are positive (+,+)
- Quadrant II: x coordinate is negative, but y coordinate is positive (-,+)
- Quadrant III: Both x and y coordinates are negative (-,-)
- Quadrant IV: x coordinate is positive, but y coordinate is negative (+,-)
3. Since the ordered pair has opposite sign coordinates, it cannot be in either Quadrant I or Quadrant III because both coordinates must share the same sign. It also cannot be in Quadrant II or Quadrant IV because they require one coordinate to be positive and the other to be negative.
Therefore, an ordered pair with opposite sign coordinates does not lie in any quadrant on a cartesian plane.
In order to determine the quadrant in which the ordered pair lies, it is helpful to understand the signs of the two coordinates.
Quadrants are divided based on the signs of the x-coordinate (horizontal) and y-coordinate (vertical).
In this case, since the coordinates have opposite signs, it means that one of the coordinates is positive and the other is negative.
If the x-coordinate is positive and the y-coordinate is negative, the ordered pair lies in the fourth quadrant.
Conversely, if the x-coordinate is negative and the y-coordinate is positive, the ordered pair lies in the second quadrant.
Overall, the quadrant where the ordered pair lies depends on whether the positive coordinate is the x-coordinate or the y-coordinate.