Step-by-step explanation: Sure, let's go through the explanation step-by-step:
1. The unit circle is divided into four quadrants:
- Quadrant I: Positive x and positive y
- Quadrant II: Negative x and positive y
- Quadrant III: Negative x and negative y
- Quadrant IV: Positive x and negative y
2. The x-axis and y-axis are also important reference points on the unit circle.
3. For each point given, we need to determine which quadrant it belongs to, or if it lies on the x-axis or y-axis.
4. Let's go through the points one by one:
- $(0,0)$: This point lies at the origin, where both the x-axis and y-axis intersect, so it belongs to both the x-axis and y-axis.
- $(1,2)$: This point has positive x and positive y coordinates, so it belongs to Quadrant I.
- $(1,-2)$: This point has positive x and negative y coordinates, so it belongs to Quadrant IV.
- $(-2,1)$: This point has negative x and positive y coordinates, so it belongs to Quadrant II.
- $(-1,-2)$: This point has negative x and negative y coordinates, so it belongs to Quadrant III.
- $(0,-2)$: This point has zero x-coordinate and negative y-coordinate, so it belongs to the y-axis.
- $(-2,0)$: This point has negative x-coordinate and zero y-coordinate, so it belongs to the x-axis.
- $(7,9)$: This point has positive x and positive y coordinates, so it belongs to Quadrant I.
5. Based on the analysis, I have filled in the table with ticks (✓) for the corresponding quadrants or axes where each point belongs.
The key is to carefully examine the sign and magnitude of the x and y coordinates to determine the quadrant or axis where the point is located on the unit circle.
