graphing the coordinate plane
The coordinates of an ordered pair have opposite signs. In which quadrant(s) must the ordered pair lie? Explain.
An ordered pair with opposite signs means that one coordinate is positive and the other is negative.
In the coordinate plane, the positive x-axis is to the right of the origin and the positive y-axis is above the origin.
Quadrant I is where both coordinates are positive. Quadrant II is where the x-coordinate is negative and the y-coordinate is positive. Quadrant III is where both coordinates are negative. Quadrant IV is where the x-coordinate is positive and the y-coordinate is negative.
Therefore, an ordered pair with opposite signs can only lie in either quadrant II or IV since those are the only quadrants where the signs of the coordinates differ.
The coordinates of an ordered pair have opposite signs. In which quadrant(s) must the ordered pair lie? Explain.
An ordered pair with opposite signs means that one coordinate is positive and the other is negative. In the coordinate plane, the positive x-axis is to the right of the origin and the positive y-axis is above the origin. The negative x-axis is to the left of the origin and the negative y-axis is below the origin.
Quadrant I is where both coordinates are positive. Quadrant II is where the x-coordinate is negative and the y-coordinate is positive. Quadrant III is where both coordinates are negative. Quadrant IV is where the x-coordinate is positive and the y-coordinate is negative.
Therefore, an ordered pair with opposite signs can only lie in either quadrant II or IV since those are the only quadrants where the signs of the coordinates differ. For example, (-3, 5) would be in quadrant II and (1, -7) would be in quadrant IV.
The coordinates of an ordered pair have opposite signs. In which quadrant(s) must the ordered pair lie? Explain.
An ordered pair with opposite signs means that one coordinate is positive and the other is negative. In the coordinate plane, the positive x-axis is to the right of the origin and the positive y-axis is above the origin. The negative x-axis is to the left of the origin and the negative y-axis is below the origin.
Quadrant I is where both coordinates are positive. Quadrant II is where the x-coordinate is negative and the y-coordinate is positive. Quadrant III is where both coordinates are negative. Quadrant IV is where the x-coordinate is positive and the y-coordinate is negative.
Thus, an ordered pair with opposite signs can only lie in quadrant II or quadrant IV because they are the only quadrants where the signs of the coordinates are opposite from each other. For example, (-4,2) would be in quadrant II, and (3,-5) would be in quadrant IV.
To determine in which quadrant(s) an ordered pair with opposite signs must lie, we first need to understand the layout of the coordinate plane.
The coordinate plane is a two-dimensional plane formed by two perpendicular number lines called the x-axis and the y-axis. The intersection of these two lines is called the origin, denoted by the point (0, 0). The x-axis represents the horizontal direction, with positive values to the right of the origin and negative values to the left. The y-axis represents the vertical direction, with positive values above the origin and negative values below.
The coordinate plane is divided into four quadrants: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV.
- Quadrant I: Consists of all the points with both x and y coordinates positive.
- Quadrant II: Consists of all the points with x coordinates negative and y coordinates positive.
- Quadrant III: Consists of all the points with both x and y coordinates negative.
- Quadrant IV: Consists of all the points with x coordinates positive and y coordinates negative.
Now, if an ordered pair has opposite signs, it means one coordinate is positive while the other is negative.
For example, let's consider an ordered pair (-3, 4). The x-coordinate is negative (-3), indicating that it falls to the left of the origin. The y-coordinate is positive (4), indicating that it falls above the origin. Hence, this ordered pair lies in Quadrant II.
In general, if the x-coordinate is negative while the y-coordinate is positive, the ordered pair lies in Quadrant II. Similarly, if the x-coordinate is positive while the y-coordinate is negative, the ordered pair lies in Quadrant IV.
Therefore, an ordered pair with opposite signs must lie in either Quadrant II or Quadrant IV.