A graph is divided into four quadrants by the x-axis and y-axis. These quadrants are labeled as Quadrant I, Quadrant II, Quadrant III, and Quadrant IV. Each quadrant has specific characteristics based on the signs of the x and y coordinates of points within them.
1. **Quadrant I**: Both the x and y coordinates are positive (x > 0, y > 0).
2. **Quadrant II**: The x coordinate is negative, and the y coordinate is positive (x < 0, y > 0).
3. **Quadrant III**: Both the x and y coordinates are negative (x < 0, y < 0).
4. **Quadrant IV**: The x coordinate is positive, and the y coordinate is negative (x > 0, y < 0).
To determine which quadrant a point will lie in without graphing it, you can follow these steps:
1. **Identify the Coordinates**: Look at the (x, y) coordinates of the point.
2. **Check the Sign of the x-coordinate**: Determine if the x-coordinate is positive or negative.
3. **Check the Sign of the y-coordinate**: Determine if the y-coordinate is positive or negative.
4. **Determine the Quadrant**: Based on the signs of the x and y coordinates, identify the quadrant using the characteristics mentioned above.
For example, if you have a point (3, -4), the x-coordinate is positive (3 > 0), and the y-coordinate is negative (-4 < 0). Therefore, this point lies in Quadrant IV.
By following these steps, you can easily determine the quadrant of any point without the need for graphing.