If the point (a,b) is in Quadrant II and `|a| - |b| > 0`, then which one of the following is true?

Options

A. `a gt 0`
B. `b gt 0`
C. `a gt b`
D. `a + b lt 0`

Answer

To solve the problem, we need to analyze the conditions given and determine which statement is true based on the properties of the coordinates in Quadrant II.

### Step-by-Step Solution:

1. **Identify the Quadrant Properties**:
- In Quadrant II, the x-coordinate (a) is negative, and the y-coordinate (b) is positive. Therefore, we have:
\[ a < 0 \quad \text{and} \quad b > 0 \]

2. **Analyze the Given Condition**:
- We are given the condition \( |a| - |b| > 0 \). Since \( a \) is negative, \( |a| = -a \) and since \( b \) is positive, \( |b| = b \). Thus, we can rewrite the condition as:
\[ -a - b > 0 \]
- This simplifies to:
\[ -a > b \quad \text{or} \quad a < -b \]

3. **Interpret the Result**:
- From \( a < -b \), we can conclude that \( a \) is less than the negative of \( b \). Since \( b > 0 \), this means that \( -b < 0 \) and hence \( a < -b \) indicates that \( a \) is more negative than \( -b \).

4. **Combine with Quadrant Properties**:
- We know that \( a < 0 \) and \( b > 0 \). Therefore, we can analyze the sum \( a + b \):
\[ a + b < 0 \quad \text{(since \( a < -b \))} \]
- This indicates that the sum of the coordinates is negative.

5. **Conclusion**:
- The only statement that aligns with our findings is that \( a + b < 0 \). Thus, this is the true statement based on the conditions provided.

### Final Answer:
The correct statement is:
\[ a + b < 0 \]