Question

Take four points P, Q, R, S in a plane. Draw lines by joining different pairs of points. How many lines can you draw in the following cases?
(i) No three of them are collinear
(ii) Three of these points are collinear.

Answer 1

According to the question, we have points P, Q, R and S in a plane.

(i) When no three of them are collinear:

We can draw 6 lines in total. They are as follows:
a by taking P and R
b by taking Q and S
c by taking P and Q
d by taking R and S
e by taking P and S
f by taking Q and R



(ii) When three points are collinear:

Let P, Q and R be collinear.
Now, we can draw 4 lines in total. They are as follows:

l by taking P and S
m by taking Q and S
n by taking R and S
q by taking P, Q and R