Statement-1: The locus of point z satisfying `|(3z+i)/(2z+3+4i)|=3/2` is a straight line.
Statement-2 : The locus of a point equidistant from two fixed points is a straight line representing the perpendicular bisector of the segment joining the given points.

Options

A. Statement-1 is True, Statement-2 is True: Statement-2 is a correct exp,anation for statement-1.
B. Statement-1 is true, statement -2 is true, Statement-2 is not a correct explanation for statement-1.
C. Statement-1 is True, statement-2 is false,
D. statement-1 is False, Statement-2 is true.

Answer

To solve the problem, we need to analyze the given statements and derive the necessary conclusions step by step.

### Step-by-Step Solution:

1. **Understanding the Given Condition**:
We start with the condition given in statement 1:
\[ \left| \frac{3z + i}{2z + 3 + 4i} \right| = \frac{3}{2} \]

2. **Using the Property of Modulus**:
We can use the property of modulus that states:
\[ \left| \frac{a}{b} \right| = \frac{|a|}{|b|} \]
Therefore, we can rewrite the equation as:
\[ \frac{|3z + i|}{|2z + 3 + 4i|} = \frac{3}{2} \]

3. **Cross-Multiplying**:
Cross-multiplying gives us:
\[ 2|3z + i| = 3|2z + 3 + 4i| \]

4. **Dividing Both Sides**:
Dividing both sides by 3 and 2 respectively, we get:
\[ \frac{|3z + i|}{3} = \frac{|2z + 3 + 4i|}{2} \]

5. **Setting Up the Equidistance Condition**:
Let \( z = x + yi \) where \( x \) and \( y \) are real numbers. We can express the moduli as:
\[ |3z + i| = |3(x + yi) + i| = |3x + (3y + 1)i| = \sqrt{(3x)^2 + (3y + 1)^2} \]
and
\[ |2z + 3 + 4i| = |2(x + yi) + 3 + 4i| = |(2x + 3) + (2y + 4)i| = \sqrt{(2x + 3)^2 + (2y + 4)^2} \]

6. **Substituting Back**:
Substitute these expressions back into our equation:
\[ 2\sqrt{(3x)^2 + (3y + 1)^2} = 3\sqrt{(2x + 3)^2 + (2y + 4)^2} \]

7. **Squaring Both Sides**:
To eliminate the square roots, we square both sides:
\[ 4((3x)^2 + (3y + 1)^2) = 9((2x + 3)^2 + (2y + 4)^2) \]

8. **Expanding and Simplifying**:
Expanding both sides leads to a quadratic equation in \( x \) and \( y \). After simplification, we will find that this represents a straight line.

9. **Conclusion**:
Since we have shown that the locus of \( z \) satisfying the given condition is indeed a straight line, statement 1 is true.

10. **Verifying Statement 2**:
Statement 2 states that the locus of a point equidistant from two fixed points is a straight line, which is a well-known theorem in geometry. Therefore, statement 2 is also true.

11. **Final Conclusion**:
Since both statements are true and statement 2 correctly explains statement 1, we conclude that:
- Statement 1 is true.
- Statement 2 is true.
- Statement 2 is a correct explanation of statement 1.