How many planes can pass through any three arbitary points ?

Options

A. 1
B. 2
C. 3
D. 0

Answer

To determine how many planes can pass through any three arbitrary points, we need to consider the arrangement of these points: whether they are collinear or non-collinear.

### Step-by-Step Solution:

1. **Understanding Collinear Points**:
- If the three points are collinear, it means they lie on the same straight line. In this case, an infinite number of planes can be drawn through these points because you can create a plane at any angle to the line formed by the three points.

**Hint**: Remember that collinear points can always be connected by a single line.

2. **Understanding Non-Collinear Points**:
- If the three points are non-collinear, it means they do not all lie on the same straight line. In this case, these three points define a unique plane. No matter how you position the points, as long as they are not on the same line, they will always create one distinct plane.

**Hint**: Visualize how three points can form a triangle; the plane is defined by the triangle they create.

3. **Conclusion**:
- Since the question does not specify whether the points are collinear or non-collinear, we can conclude that if we assume the points are non-collinear (which is a common assumption unless stated otherwise), then only one plane can pass through these three points.

### Final Answer:
- Therefore, the answer is **1 plane** can pass through three arbitrary points, assuming they are non-collinear.