Check the change in y over the change in x. From R to B: (–5 – –1) / (–2 – –5) = –4/3. From B to C: (–12 – –5) / (4 – –2) = –7/6. Slopes differ, so they are not collinear.
Use your method (from Problem 6) to check if the points R (– 5, – 1), B (– 2, – 5) and C (4, – 12) are on the same straight line. Now plot both sets of points and check your answers.
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Using the slope method, we calculate the steepness between pairs of points. The slope of segment RB is calculated as –4/3, which is approximately –1.33. The slope of segment BC is calculated as –7/6, which is approximately –1.16. Since these two slopes are not identical, the direction of the line changes at point B. Therefore, the points R (–5, –1), B (–2, –5) and C (4, –12) do not lie on a straight line.
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/