Yes, they are collinear. One method is comparing the ratio of coordinates (y/x). For M, –4 divided by –3 equals 4/3; for G, 8 divided by 6 equals 4/3. Since ratios match, they are on one line.
Are the points M (– 3, – 4), A (0, 0) and G (6, 8) on the same straight line? Suggest a method to check this without plotting and joining the points.
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To check if points are collinear without plotting, you can use the ratio method. For points passing through the origin A (0, 0), if the ratio of the y-coordinate to the x-coordinate for all other points is equal, they lie on the same straight line. For the point M (–3, –4), the ratio is 4/3 and for the point G (6, 8), the ratio is also 4/3. Thus, M, A and G are collinear.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/