Plot the following points and check whether they are collinear or not (2 3) (3 2) (1 -5)

Plot the following points and check whether they are collinear or not:

(1, 3), (– 1, – 1), (– 2, – 3)

Plotting the points P(1, 3), Q(–1, –1) and R(–2, – 3) on the graph paper and join these points, we get a straight line. Hence, these points are collinear.

Concept: Plotting a Point in the Plane If Its Coordinates Are Given.

Is there an error in this question or solution?

Page 2

Plotting the points P(1, 1), 0 (2, – 3) and R(–1, –2) on the graph paper and join these three points, we get three lines i.e., the given points do not lie on the same line. So, given points are not collinear.

Page 3

Plot the following points and check whether they are collinear or not:

(0, 0), (2, 2), (5, 5)

Plotting the points 0 (0, 0), A (2,2)and 6 (5, 5)on the graph paper and join these points, we get a straight line. Hence, given points are collinear.

Concept: Plotting a Point in the Plane If Its Coordinates Are Given.

Is there an error in this question or solution?

Solution:

Given, the points are (1, 1), (2, -3) and (-1, -2)

We have to determine if the points are collinear or not.

Let the point (1, 1) be P

The perpendicular distance of the point P from the x-axis is 1 unit and y-axis is 1 unit.

The point P lies in the first quadrant.

Let the point (2, -3) be Q

The perpendicular distance of the point Q from the x-axis is 3 units and y-axis is 2 units.

The point Q lies in the fourth quadrant.

Let the point (-1, -2) be R

The perpendicular distance of the point R from the x-axis is 2 units and the y-axis is 1 unit.

The point R lies in the third quadrant.

On plotting the points on the graph,

On joining the points P, Q and R we observe that the points do not lie on the straight line.

Therefore, the points are not collinear.

✦ Try This: Plot the following points and check whether they are collinear or not : (2, 2), (3, -4), (- 2, - 3)

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 3

NCERT Exemplar Class 9 Maths Exercise 3.3 Problem 4(ii)

Summary:

On plotting the points (1, 1) (2, -3) and (-1, -2) we observe that the points do not lie on the straight line. This implies the given points are not collinear

☛ Related Questions:

The points that are collinear are those that are on the same straight line or on a single line. In Euclidean geometry, two or more points on a line that are close to or far from each other are said to be collinear.

(i)

The points (1, 3), (– 1, – 1), (– 2, – 3) lie in a straight line,

Hence, the points are collinear.

(ii)

The points (1, 1), (2, – 3), (– 1, – 2) lie in a straight line,

Hence, the points are not collinear.

(iii)

The points (0, 0), (2, 2), (5, 5) lie in a straight line,

Hence, the points are collinear.

(i) (1, 3), (– 1, – 1), (– 2, – 3)

The points (1, 3), (– 1, – 1), (– 2, – 3) lie in a straight line,

Thus, the given points are collinear.