Describe the locus of point at distances less than or equal to 2.5 cm from a given point.

Answer

To describe the locus of a point at distances less than or equal to 2.5 cm from a given point, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Point**:
- Let's denote the given point as \( O \). This point is fixed and serves as the center for our locus.

2. **Understand the Concept of Locus**:
- The locus of a point is defined as the set of all positions that the point can occupy under certain conditions. In this case, the condition is that the point must be at a distance less than or equal to 2.5 cm from point \( O \).

3. **Draw a Circle**:
- To represent the locus, we will draw a circle with center \( O \) and a radius of 2.5 cm. This circle will represent all the points that are exactly 2.5 cm away from point \( O \).

4. **Include Points Inside the Circle**:
- Since the distance can be less than or equal to 2.5 cm, the locus will include all points that lie inside the circle as well as the points on the circumference of the circle.

5. **State the Locus**:
- Therefore, we can conclude that the locus of point \( P \) (the point that can move) is the area inside the circle and the circumference of the circle with radius 2.5 cm centered at point \( O \).

### Final Statement:
The locus of point \( P \) is the set of all points that lie inside and on the circumference of a circle with radius 2.5 cm and center at point \( O \).

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