Question

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from these 8 points?

• A. 26
• B. 28
• C. 27
• D. 25

Hint:

When points are collinear, subtract the number of lines formed by the collinear points from the total number of lines.

Answer 1

The Correct Option is A

We are given that there are 8 points, 3 of which are collinear. Step 1: Count total number of lines The total number of lines that can be drawn by joining any two points from the 8 points is given by the combination: \[ \binom{8}{2} = \frac{8 \times 7}{2} = 28 \] Step 2: Subtract collinear points The 3 collinear points can only form 1 line, so we subtract the number of lines formed by these 3 points: \[ 28 - 3 = 26 \] Thus, the correct answer is 26.