Use absolute value concept to find the distance between :
a. two points `S` and `T` such that, point `S` is `9` m away from the origin towards right and point 'T'
is 2 m away from the origin in the opposite direction.
b. the points : 26 and -17.

Answer

To solve the problem step by step, we will find the distances as described in the question.

### Part a: Finding the distance between points S and T

1. **Identify the positions of points S and T**:
- Point S is 9 meters away from the origin towards the right. This means S is at position +9 on the number line.
- Point T is 2 meters away from the origin in the opposite direction (to the left). This means T is at position -2 on the number line.

2. **Write the positions of S and T**:
- Position of S: \( S = +9 \)
- Position of T: \( T = -2 \)

3. **Calculate the distance between S and T**:
- The distance between two points on a number line can be calculated using the formula:
\[ \text{Distance} = |S - T| \]
- Substitute the values of S and T:
\[ \text{Distance} = |9 - (-2)| \]
- Simplifying further:
\[ \text{Distance} = |9 + 2| = |11| = 11 \text{ meters} \]

### Part b: Finding the distance between the points 26 and -17

1. **Identify the positions of the points**:
- Point A is at position 26.
- Point B is at position -17.

2. **Write the positions of A and B**:
- Position of A: \( A = 26 \)
- Position of B: \( B = -17 \)

3. **Calculate the distance between A and B**:
- Using the distance formula:
\[ \text{Distance} = |A - B| \]
- Substitute the values of A and B:
\[ \text{Distance} = |26 - (-17)| \]
- Simplifying further:
\[ \text{Distance} = |26 + 17| = |43| = 43 \text{ units} \]

### Final Answers:
- a. The distance between points S and T is **11 meters**.
- b. The distance between the points 26 and -17 is **43 units**.

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