Three non collinear points A, B and C lie on the same plane. How many different straight lines can be drawn by joining these three points pairwise?

Introduction / Context:
This question checks basic understanding of how many straight lines can be formed from a set of given points. When points are non collinear, no three points lie on the same straight line. Such questions are common in elementary geometry and combinatorics, and they focus on reasoning about pairs of points.

Given Data / Assumptions:
There are three points: A, B and C. The points are non collinear, meaning no single straight line passes through all three points. A straight line is uniquely determined by any two distinct points. No other hidden constraints are mentioned.

Concept / Approach:
Any straight line in a plane can be defined by choosing two distinct points and joining them. Therefore, the number of distinct lines that can be formed from a set of points is the number of distinct pairs of points. Since the three points are non collinear, each pair forms a different line. Hence, we only need to count the number of pairs of points using a simple combination formula or direct reasoning.

Step-by-Step Solution:
Step 1: List all the possible pairs of points: (A, B), (B, C) and (A, C). Step 2: Each pair corresponds to a unique line because no three points are collinear. Step 3: Count the number of such pairs. There are exactly 3 pairs. Step 4: Alternatively, use the combination formula nC2 where n = 3. Step 5: Compute 3C2 = 3 * 2 / 2 = 3. Step 6: Therefore, the number of distinct lines formed is 3.

Verification / Alternative check:
You can also sketch three non collinear points and manually draw lines between each pair. You will see one line between A and B, one between B and C, and one between A and C. There is no way to draw any additional line that passes through two of these points without coinciding with one of the already drawn lines. This visual method confirms that the correct count is 3 distinct lines.

Why Other Options Are Wrong:
The value 6 could arise from mistakenly counting each pair twice with reversed order (for example, AB and BA as different). The value 2 suggests missing one line segment altogether. The value 4 suggests adding a line that does not correspond to a pair of given points. Only 3 correctly counts the unique lines determined by pairs of the three points A, B and C.

Common Pitfalls:
Students sometimes confuse segments and lines, or they overcount by considering direction as important when it is not. Others might try to imagine additional lines passing through a single point, but by definition we only consider lines determined by at least two of the given points. Remember that for n distinct points with no three collinear, the number of distinct lines is always nC2, so for 3 points it must be 3.

Final Answer:
The number of different straight lines that can be drawn through the three non collinear points A, B and C is 3.