Number of straight lines from 10 points with 7 collinear: How many distinct straight lines can be formed?

Introduction / Context:Distinct lines arise from pairs of points, but when many points are collinear, all pairs among them correspond to the same line and must not be overcounted.

Given Data / Assumptions:10 points total; 7 on one line; assume the other 3 are in general position relative to the 7 and each other.

Concept / Approach:Total potential lines from all pairs minus the overcount among the collinear 7, then add back that single line once.

Step-by-Step Solution:

Verification / Alternative check:List categories: the one big line from the 7, lines from an off-line point to each of the 7, and lines among off-line points — totals reconcile to 25.

Why Other Options Are Wrong:26 or 21 result from missing either the subtraction or the add-back of one line.

Common Pitfalls:Forgetting to add the unique collinear line back after subtracting its pairs.

Final Answer:25