Question

Identify the given figures as collinear or non – collinear points.
(a)

(b)

(c)

(d)

i. (a) and (c) are collinear; (b) and (d) are non collinear
ii. (a), (b) and (c) are collinear; (d) is non collinear
iii. (a) and (d) are collinear; (b) and (c) are non collinear
iv. (b) and (c) are collinear; (a) and (d) are non collinear

Answer 1

Hint: Before solving this question, we must know about Collinear Points and Non – Collinear Points.
COLLINEAR POINTS: Three or more points are said to be collinear if they lie on a single line. Also, the line on which the collinear points lie must be straight.
NON – COLLINEAR POINTS: Three or more points are said to be non – collinear if they do not lie on a single, straight line.

Complete step-by-step answer:
For solving this question, we will have to consider every option.
So, in this question, we need to find the collinear and non – collinear points from the options provided. We will check whether the line, on which the points are lying, is straight or not.
If the points are lying on a straight line, then the points are collinear, otherwise, they are non – collinear.
Let us now identify which of the above points are collinear and which are non collinear.
A. The points in the figure (a) are lying on a straight line. Therefore, they are collinear points.
B. The points in the figure (b) are not lying on a straight line, i.e. the line on which they are lying is not straight. Therefore, they are non-collinear points.
C. The points in the figure (c) are lying on a straight line. Therefore, they are collinear points.
D. The points in the figure (d) are not lying on a straight line, i.e. the line on which they are lying is not a straight one. Therefore, they are non-collinear points.
We can observe that the points in the figure (a) and (c) are collinear and the points in the figure (b) and (d) are non collinear.
Therefore, the answer of this question is (i) (a) and (c) are collinear; (b) and (d) are non collinear.

NOTE:- One must always remember about collinear points and non collinear points as they can come in handy.
Also, remember that collinear points are the points that lie on a straight line and non collinear are the points that do not lie on a straight line.