Three points A B and C are collinear . If points C , P and Q are collinear then will the point A,B,C,P and Q also be collinear ? Explain your answer with reasons:

Answer

To determine whether points A, B, C, P, and Q are collinear given the conditions in the question, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding Collinearity**:
- Points are said to be collinear if they lie on the same straight line. In this case, we start with points A, B, and C being collinear, which means they are on the same line.

2. **Introducing Points P and Q**:
- We are given that points C, P, and Q are also collinear. This means that points C, P, and Q lie on another straight line.

3. **Analyzing the Relationship**:
- Since points A, B, and C are collinear, we can visualize them on a straight line. However, the line that contains points C, P, and Q may or may not be the same as the line containing A, B, and C.

4. **Considering Different Scenarios**:
- If the line containing C, P, and Q is the same as the line containing A, B, and C, then all five points (A, B, C, P, and Q) will be collinear.
- However, if the line containing C, P, and Q is different from the line containing A, B, and C, then points A, B, C, P, and Q will not be collinear.

5. **Conclusion**:
- Therefore, we cannot definitively say that points A, B, C, P, and Q are collinear without additional information about the specific arrangement of points P and Q in relation to points A, B, and C. The collinearity of A, B, C, P, and Q depends on whether the line CPQ coincides with line ABC.

### Final Answer:
Points A, B, C, P, and Q may or may not be collinear. They will be collinear only if the line containing points C, P, and Q is the same as the line containing points A, B, and C.