Final Answer:
The answer is (a) Infinitely many.
Step-by-step explanation:
For any three non-colinear points, you can draw infinitely many lines such that each line passes through two of the given points. This is based on the fundamental geometric principle that any two distinct points uniquely determine a line. With three non-colinear points, each pair of points forms a unique line, resulting in a multitude of lines passing through these points. Therefore, the correct answer is (a) Infinitely many.
Understanding the relationship between points and lines in geometry is fundamental to solving problems like these. For any two distinct points, there is exactly one line that connects them. Extending this concept to three non-colinear points, each pair of points forms a unique line. The resulting set of lines is infinite, as each pair of points can be connected by a line, providing numerous possibilities.
In conclusion, the answer is that there are infinitely many lines that can be drawn through three non-colinear points. This is a fundamental concept in geometry, emphasizing the unique relationship between points and lines and showcasing the versatility of configurations that can be formed with three distinct points.