The coordinates of an ordered pair have 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.
For example, the ordered pair (-3, 5) has opposite signs because -3 is negative and 5 is positive.
Since the signs of the coordinates are opposite, the ordered pair must lie in either the second or fourth quadrant of the cartesian plane. This is because the second and fourth quadrants are the only quadrants where x and y have opposite signs.
In the second quadrant, x is negative and y is positive. In the fourth quadrant, x is positive and y is negative.
So, to determine in which quadrant the ordered pair lies, we would need to know which coordinate is positive and which is negative. If the x-coordinate is negative and the y-coordinate is positive, the ordered pair lies in quadrant II. If the x-coordinate is positive and the y-coordinate is negative, the ordered pair lies in quadrant IV.
To determine in which quadrant an ordered pair lies, we need to consider the signs of its coordinates.
The four quadrants are numbered in a counterclockwise direction. The positive x-axis is to the right, and the positive y-axis is upward.
If the x-coordinate of an ordered pair is positive and the y-coordinate is positive, it falls in the first quadrant (Q1).
If the x-coordinate is negative and the y-coordinate is positive, it falls in the second quadrant (Q2).
If the x-coordinate is negative and the y-coordinate is negative, it falls in the third quadrant (Q3).
If the x-coordinate is positive and the y-coordinate is negative, it falls in the fourth quadrant (Q4).
Now, let's apply this information to an ordered pair with opposite signs. When an ordered pair has opposite signs, it means that one coordinate is positive while the other is negative.
If an ordered pair has a positive x-coordinate and a negative y-coordinate, it falls in the fourth quadrant (Q4). This is because the positive x-coordinate places it to the right of the origin, and the negative y-coordinate places it below the origin.
To summarize, when the coordinates of an ordered pair have opposite signs, the ordered pair lies in the fourth quadrant (Q4).
An ordered pair consists of two coordinates, typically denoted as (x, y). In this case, we know that the coordinates have opposite signs, meaning one coordinate is positive and the other is negative.
Let's consider the four quadrants on a Cartesian plane:
- The first quadrant (Q1) is located in the top right, where both x and y are positive.
- The second quadrant (Q2) is located in the top left, where x is negative and y is positive.
- The third quadrant (Q3) is located in the bottom left, where both x and y are negative.
- The fourth quadrant (Q4) is located in the bottom right, where x is positive and y is negative.
Since one coordinate is positive and the other is negative, we can determine that the ordered pair lies in either Q2 or Q4.
To figure out whether it is Q2 or Q4, we would need to know the specific values of the coordinates. If the positive coordinate is greater than the negative one, the ordered pair would lie in Q4. If the negative coordinate is greater, then the ordered pair would lie in Q2.