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

Text Solution

Solution : (i) Plotting the points P(1,2), 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. <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_IX_C03_S01_029_S01.png" width="80%"> (ii) Plotting the points P(1,1), Q(2,-3) and R(-1,-2) on the graph paper and join these three points, we get three lines i.e., given points do not lie on the same line. So, given points are not collinear. <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_IX_C03_S01_029_S02.png" width="80%"> (iii) Plotting the points O(0,0) , A(2,2) and B(5,5) on the graph paper and join the these points we get a straight line. Hence, given points are collinear. <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_IX_C03_S01_029_S03.png" width="80%">

(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.

(ii) (1, 1), (2, – 3), (– 1, – 2)

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

Thus, the given points are not collinear.

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

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

Thus, the given points are collinear.

Was this answer helpful?

3.5 (3)

Thank you. Your Feedback will Help us Serve you better.

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.

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, 3), (-1, -1) and (-2, -3)

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

Let the point (1, 3) be P

The perpendicular distance of the point P from the x-axis is 3 units and y-axis is 1 unit.

The point P lies in the first quadrant.

Let the point (-1, -1) be Q

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

The point Q lies in the third quadrant.

Let the point (-2, -3) be R

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

The point R lies in the third quadrant.

On plotting the points on the graph,

On joining the points P, Q and R we get a straight line.

Therefore, the points are collinear.

✦ Try This: Plot the following points and check whether they are collinear or not : (1, 2), (- 2, - 2), (- 3, - 4)

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

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

Summary:

On plotting the points (1, 3) (-1, -1) and (-2, -3) and joining them we observe that all the given points lie on a straight line. This implies the given points are collinear

☛ Related Questions:

(1, 1), (2, -3), (-1, -2). Plot the following points and check whether they are collinear or not
(0, 0), (2, 2), (5, 5). Plot the following points and check whether they are collinear or not
Without plotting the points indicate the quadrant in which they will lie, if ordinate is 5 and absci . . . .