The line segment joining the points (-3,-4) and (1, -2) is
divided by Y-axis in the ratio.

Options

A. `2:3`
B. `3:2`
C. `3:1`
D. 1:3`

Answer

To find the ratio in which the Y-axis divides the line segment joining the points (-3, -4) and (1, -2), we can use the section formula. Let's go through the steps:

### Step-by-Step Solution:

1. **Identify the Points**:
We have two points, A(-3, -4) and B(1, -2).

2. **Use the Section Formula**:
The section formula states that if a point P divides the line segment joining points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of P are given by:
\[ P\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right) \]

3. **Set the X-coordinate to 0**:
Since we want to find where the line segment is divided by the Y-axis, we set the x-coordinate of point P to 0:
\[ 0 = \frac{m \cdot 1 + n \cdot (-3)}{m+n} \]

4. **Solve for the Ratio**:
This leads to the equation:
\[ m \cdot 1 + n \cdot (-3) = 0 \]
Rearranging gives:
\[ m - 3n = 0 \quad \Rightarrow \quad m = 3n \]
This indicates that the ratio \( m:n = 3:1 \).

5. **Conclusion**:
Therefore, the Y-axis divides the line segment joining the points (-3, -4) and (1, -2) in the ratio 3:1.