Question

There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?

• A. 39
• B. 40
• C. 45
• D. 21

Hint:

When dealing with collinear points, subtract the extra lines that would have been counted as distinct, as they lie on the same line.

Answer 1

The Correct Option is B

The total number of straight lines that can be formed by joining any two points from 10 points is given by the combination formula: \[ \text{Total lines} = \binom{10}{2} = \frac{10(10-1)}{2} = 45 \] However, 4 points are collinear, meaning they lie on the same straight line, and we should subtract the number of lines formed by these 4 points. The number of lines formed by the 4 collinear points is: \[ \text{Lines formed by collinear points} = \binom{4}{2} = \frac{4(4-1)}{2} = 6 \] Since all 4 collinear points form only 1 straight line, we subtract the extra 5 lines that would be counted if we treated them as distinct. Thus, the total number of distinct lines is: \[ \text{Total distinct lines} = 45 - 5 = 40 \] Therefore, the number of straight lines that can be drawn is 40.