To identify the location of each point with respect to the x-axis, y-axis, and quadrants, we can use the following information:
- Quadrant I: x > 0, y > 0
- Quadrant II: x < 0, y > 0
- Quadrant III: x < 0, y < 0
- Quadrant IV: x > 0, y < 0
- On the x-axis: y = 0 (x can be any value)
- On the y-axis: x = 0 (y can be any value)
Now, let's analyze each point:
-
Point B (0, 6):
- Located on the y-axis (since x = 0).
-
Point C (5, -2):
- x > 0 and y < 0 → Located in Quadrant IV.
-
Point D (-1, 10):
- x < 0 and y > 0 → Located in Quadrant II.
-
Point E (5, 0):
- Located on the x-axis (since y = 0).
-
Point F (-1/4, -6/1/2):
- First, simplify the second coordinate: -6/1/2 = -6 * 2/1 = -12, so the point is (-1/4, -12).
- x < 0 and y < 0 → Located in Quadrant III.
Now, we can complete the table based on the analysis:
| Point | Location | |-------|------------------| | B | y-axis | | C | Quadrant IV | | D | Quadrant II | | E | x-axis | | F | Quadrant III |
This table properly identifies where each point is located according to the provided options.