Which of the following steps of construction is incorrect while dividing a line segment of length 3.2 cm in the ratio of 3 : 5 internally.
Steps of Construction
Step I : Draw AB = 3.2 cm
Step II : Construct an acute `angle BAX`.
Step III : On AX make 3 + 5 + 1 i.e. 9 equal parts and mark them as `A_(1), A_(2),A_(3),A_(4),.........A_(9)`
Step IV : Join B to `A_(8)`. From `A_(3)` draw `A_(3)C` parallel to `A_(8)B`. Point C divides AB internally in the ratio 3 : 5.
THus, AC : CB = 3 : 5.

Options

A. Step II
B. Step III
C. Step IV
D. None of these

Answer

To divide a line segment of length 3.2 cm in the ratio of 3:5 internally, we follow these steps:

### Step-by-Step Solution:

**Step 1:** Draw the line segment AB of length 3.2 cm.
- Use a ruler to measure and draw a straight line segment from point A to point B, ensuring the length is exactly 3.2 cm.

**Step 2:** Construct an acute angle BAX.
- At point B, use a protractor to measure an acute angle (less than 90 degrees) and draw a ray AX extending from point B.

**Step 3:** Divide the ray AX into equal parts.
- Since we need to divide the line segment in the ratio of 3:5, we first calculate the total parts: 3 + 5 = 8 parts.
- Using a compass, mark off 8 equal segments along the ray AX, labeling them A1, A2, A3, A4, A5, A6, A7, A8.

**Step 4:** Join point B to point A8.
- Use a ruler to draw a straight line connecting point B to point A8.

**Step 5:** Draw a line from A3 parallel to BA8.
- From point A3, draw a line parallel to line BA8. This can be done using a set square or a protractor to ensure the lines are parallel.

**Step 6:** Mark the intersection point as C.
- The line drawn from A3 will intersect the line segment AB at point C.

**Conclusion:** Point C divides the line segment AB into two parts, AC and CB, such that the ratio AC:CB = 3:5.

### Identification of Incorrect Step:
The incorrect step in the provided construction is **Step 3**, where it states to make 9 equal parts instead of 8. The correct number of equal parts should be 8, as we are dividing the segment in the ratio of 3:5.