Chapter 1: Orienting Yourself: The Use of Coordinates

Exercise

Question

Question: 6

8 / 25

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.

Answer

1
Find the distances between each pair of points using the Baudhāyana-Pythagoras theorem.
MA = \sqrt{(0 - (-3))^2 + (0 - (-4))^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
AG = \sqrt{(6 - 0)^2 + (8 - 0)^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10
GM = \sqrt{(-3 - 6)^2 + (-4 - 8)^2} = \sqrt{(-9)^2 + (-12)^2} = \sqrt{81 + 144} = \sqrt{225} = 15
2
Compare the sum of the two smaller distances with the largest distance. If the sum is equal to the largest distance, the three points are .
Answer: Yes. The points M, A, and G lie on the same straight line.
Reason: Since MA + AG = 5 + 10 = 15 = MG, the point A lies between M and G. Therefore, M, A, and G are collinear.
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