Question

Question 1
The number of lines passing through five points such that no three of them are collinear is
a) 10
b) 5
c) 20
d) 8

Answer 1

Three or more points are said to be collinear if they lie on a single straight line.

Let A, B, C, D and E be five points such that no three of them are collinear.

Since, total number of points is $5$ and we need $2$ points to form a line.

$\therefore$ Total number of lines passing through the points is $5\times 2=10$
$\therefore$ Lines passing through these five points are AB, BC, CD, DE, EA, BE, BD, CE, AC and AD.
Hence, the number of lines are 10.