To divide a line segment AB in the ratio 5:7, first a ray AX is drawn, so that `/_BAX` is an acute angle and then at equal distances point are marked on the ray AX such that the minimum number of these points is

Options

A. 8
B. 10
C. 11
D. 12

Explanation

To divide a line segment AB in the ratio 5:7, we will follow these steps:

### Step-by-Step Solution:

1. **Draw the Line Segment AB**:
- Start by drawing a line segment AB of any convenient length.

2. **Draw a Ray AX**:
- At point A, draw a ray AX such that the angle ∠BAX is an acute angle. This ray will be used to mark points at equal distances.

3. **Determine the Ratio**:
- The given ratio is 5:7. Here, m = 5 and n = 7.

4. **Calculate the Total Number of Parts**:
- To divide the segment in the ratio m:n, we need to calculate the total number of parts, which is m + n.
- So, total parts = 5 + 7 = 12.

5. **Mark Points on Ray AX**:
- Mark 12 points (let's call them P1, P2, P3, ..., P12) on the ray AX at equal distances.

6. **Locate the Division Points**:
- From point A, count 5 points (P1 to P5) for the first segment and then from point P5, count another 7 points (P6 to P12) for the second segment.

7. **Draw the Line Segment**:
- Finally, draw a line from point B to the point where the 5th point (P5) is located on the ray AX. This point will divide the line segment AB in the ratio 5:7.

### Final Answer:
The minimum number of points to be marked on ray AX is **12**.

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