Let's analyze the given points one by one to determine in which quadrant they lie or if they are on one of the coordinate axes.
Given Points:
[tex]\[ A=(2,-6) \][/tex]
[tex]\[ B=(-8,3) \][/tex]
[tex]\[ C=(0,1) \][/tex]
[tex]\[ D=(-3,-1) \][/tex]
[tex]\[ E=(1,0) \][/tex]
### Analyzing Points
Point A: (2, -6)
- The x-coordinate is positive, and the y-coordinate is negative.
- This means point A is in Quadrant IV.
Point B: (-8, 3)
- The x-coordinate is negative, and the y-coordinate is positive.
- As such, point B is in Quadrant II.
Point C: (0, 1)
- The x-coordinate is 0, and the y-coordinate is positive.
- Since point C lies on the y-axis, but not at the origin, it is on the y-axis.
Point D: (-3, -1)
- The x-coordinate and the y-coordinate are both negative.
- This means point D is in Quadrant III.
Point E: (1, 0)
- The x-coordinate is positive, and the y-coordinate is 0.
- As point E lies on the x-axis, but not at the origin, it is on the x-axis.
### Summary of Points
- A=(2,-6) -> Quadrant IV
- B=(-8,3) -> Quadrant II
- C=(0,1) -> none, because the point is on the y-axis
- D=(-3,-1) -> Quadrant III
- E=(1,0) -> none, because the point is on the x-axis
From the options given:
- Quadrant III - This corresponds to point D.
- none, because the point is on the y-axis - This corresponds to point C.
- Quadrant I - This is not applicable to any of the given points.
- none, because the point is on the y-axis - Already corresponds to point C.
- Quadrant I - Not applicable.
- none, because the point is on the x-axis - This corresponds to point E.
- Quadrant IV - This corresponds to point A.
- Quadrant IV - Already corresponds to point A.
- Quadrant III - Already corresponds to point D.
- Quadrant II - This corresponds to point B.
- Quadrant II - Already corresponds to point B.
- Quadrant IV - Already corresponds to point A.
- none, because the point is on the y-axis - Already corresponds to point C.
- none, because the point is on the x-axis - Already corresponds to point E.
So, for the specific question about point B: It lies in Quadrant II.
