A `bar (AB)` is 10.2 cm long. If P is the mid point of AB, then the length of `bar(PB)` is ____

Options

A. 4.8 cm
B. 8.2 cm
C. 5.1 cm
D. 5.2 cm

Answer

To find the length of the segment PB when P is the midpoint of the segment AB, follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Length of AB**:
The length of the bar (line segment) AB is given as 10.2 cm.

2. **Understand the Midpoint**:
Since P is the midpoint of AB, it divides the segment AB into two equal parts. This means that the lengths of segments PA and PB are equal.

3. **Set Up the Equation**:
Let the length of PB be denoted as x. Since PA is equal to PB, we can also denote PA as x. Therefore, we can express the total length of AB as:
\[ AB = PA + PB = x + x = 2x \]

4. **Substitute the Known Length**:
We know that the total length of AB is 10.2 cm. So, we can write the equation:
\[ 2x = 10.2 \]

5. **Solve for x**:
To find the length of PB (which is x), divide both sides of the equation by 2:
\[ x = \frac{10.2}{2} \]

6. **Calculate the Value**:
Performing the division gives:
\[ x = 5.1 \text{ cm} \]

7. **Conclusion**:
Therefore, the length of the segment PB is 5.1 cm.

### Final Answer:
The length of bar PB is **5.1 cm**.

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