In what ratio is the line joining P(5, 3) and Q(-5, 3) divided by the y-axis? Also find the coordinates of the point of intersection.

Answer

To solve the problem of finding the ratio in which the line joining points P(5, 3) and Q(-5, 3) is divided by the y-axis, as well as the coordinates of the point of intersection, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Points**:
Let P(5, 3) and Q(-5, 3) be the two points.

2. **Assume the Ratio**:
Since the ratio in which the line is divided by the y-axis is unknown, we can assume it to be 1:k.

3. **Use the Section Formula**:
The section formula states that if a point divides the line segment joining two points (x1, y1) and (x2, y2) in the ratio m:n, then the coordinates of the point (x, y) are given by:
\[ x = \frac{mx_2 + nx_1}{m+n}, \quad y = \frac{my_2 + ny_1}{m+n} \]
Here, we know that the point of intersection lies on the y-axis, which means the x-coordinate is 0.

4. **Set Up the Equation for x-coordinate**:
Using the section formula for the x-coordinate:
\[ 0 = \frac{(1)(-5) + (k)(5)}{1+k} \]
This simplifies to:
\[ 0 = -5 + 5k \]
Rearranging gives:
\[ 5k = 5 \implies k = 1 \]

5. **Determine the Ratio**:
Since we assumed the ratio to be 1:k, and we found k = 1, the ratio in which the line is divided by the y-axis is:
\[ 1:1 \]

6. **Calculate the y-coordinate**:
Now, we can find the y-coordinate using the section formula:
\[ y = \frac{(1)(3) + (1)(3)}{1+1} = \frac{3 + 3}{2} = \frac{6}{2} = 3 \]

7. **Point of Intersection**:
Therefore, the coordinates of the point of intersection are:
\[ (0, 3) \]

### Final Answer:
The line joining P(5, 3) and Q(-5, 3) is divided by the y-axis in the ratio 1:1, and the coordinates of the point of intersection are (0, 3).