Point `(1,1), (1,-1), (-1, 1), (-1,-1)`

Options

A. lie in I quadrant
B. lie in III quadrant
C. lie in l and III quadrants
D. do not lie in the same quadrant

Answer

To determine which quadrants the points (1, 1), (1, -1), (-1, 1), and (-1, -1) lie in, we can analyze each point step by step.

### Step-by-Step Solution:

1. **Identify the Points:**
The points given are:
- Point A: (1, 1)
- Point B: (1, -1)
- Point C: (-1, 1)
- Point D: (-1, -1)

2. **Determine the Quadrant for Each Point:**
- **Point A (1, 1):**
- Both x and y are positive.
- This point lies in the **First Quadrant**.

- **Point B (1, -1):**
- x is positive and y is negative.
- This point lies in the **Fourth Quadrant**.

- **Point C (-1, 1):**
- x is negative and y is positive.
- This point lies in the **Second Quadrant**.

- **Point D (-1, -1):**
- Both x and y are negative.
- This point lies in the **Third Quadrant**.

3. **Summary of Quadrants:**
- Point A (1, 1) is in the **First Quadrant**.
- Point B (1, -1) is in the **Fourth Quadrant**.
- Point C (-1, 1) is in the **Second Quadrant**.
- Point D (-1, -1) is in the **Third Quadrant**.

4. **Conclusion:**
The points do not lie in the same quadrant. They are distributed across all four quadrants:
- First Quadrant: (1, 1)
- Second Quadrant: (-1, 1)
- Third Quadrant: (-1, -1)
- Fourth Quadrant: (1, -1)

Thus, the correct answer is that the points do not lie in the same quadrant.