Question

how many different straight lines can be formed by joining 12 different points on a plane of which four are collinear and the rest are non collinear?
a.16
b.32
c.61
d.64​

Answer 1

Answer:61

Step-by-step explanation:

Answer 2

Answer:

Number of lines can be formed = 61

Given problem:

How many different straight lines can be formed by joining 12 different points on a plane of which four are collinear and the rest are non collinear?

Step-by-step explanation:

Given number of points = 12 points

Number of collinear points = 4 points

Note:

Number of different lines can be formed with 'm' points in which 'n' points are collinear =  $\frac{m(m-1)}{2} - \frac{n(n-1)}{2} +1$  

Therefore, number of different lines can be formed with '12' in which '4' points are collinear points  = $\frac{12(12-1)}{2} - \frac{4(4-1)}{2} +1$  

                                             = $\frac{12(11)}{2} - \frac{4(3)}{2} +1$  

                                             = 6(11) - 2(3) +1

                                             = 66 - 6 +1 = 61