What is the locus of a point in space, which is always at a distance of 4 cm from a fixed point ?

Answer

To find the locus of a point in space that is always at a distance of 4 cm from a fixed point, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Fixed Point**:
Let's denote the fixed point as \( O \). This point is stationary and serves as the center of our locus.

**Hint**: Remember that the fixed point is the reference from which we measure the distance.

2. **Define the Moving Point**:
Let \( P \) be the point in space that is moving. According to the problem, the distance from point \( O \) to point \( P \) is always 4 cm.

**Hint**: The moving point \( P \) is the one whose path we are trying to determine.

3. **Understand the Distance Condition**:
The condition states that the distance \( OP = 4 \) cm. This means that no matter where point \( P \) moves, it must always maintain this fixed distance from point \( O \).

**Hint**: Visualize the distance as a radius extending from point \( O \).

4. **Visualize the Locus**:
As point \( P \) moves while maintaining a distance of 4 cm from point \( O \), it traces out a path. This path is a circle with a radius of 4 cm centered at point \( O \).

**Hint**: Think of how a circle is defined: all points that are a fixed distance from a center point.

5. **Conclude the Locus**:
Therefore, the locus of point \( P \) is a circle with a radius of 4 cm, centered at point \( O \).

**Hint**: Remember that the locus is essentially the set of all possible positions of point \( P \) that satisfy the distance condition.

### Final Answer:
The required locus of a point in space that is always at a distance of 4 cm from a fixed point is a circle with a radius of 4 cm centered at that fixed point.