Question 6 - End-of-Chapter Exercises - Chapter 1 Class 9 - Orienting Yourself: The Use of Coordinates (Ganita

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Question 6 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. If three points are on the exact same straight line (collinear), then Distance of the two shorter segments added together will perfectly equal the distance of the longest segment. Let’s find distance of all 3 points Distance AM Here, A (0, 0) and M (–3, –4) So, AM = √((−𝟑−𝟎)^𝟐+(−𝟒−𝟎)^𝟐 ) = √(〖(−3)〗^2+〖(−4)〗^2 ) = √(𝟑^𝟐+𝟒^𝟐 ) = √(9+16) = √25 = √(5^2 ) = 5 Distance AG Here, A (0, 0) and G (6, 8) So, AG = √((𝟔−𝟎)^𝟐+(𝟖−𝟎)^𝟐 ) = √(𝟔^𝟐+𝟖^𝟐 ) = √(36+64) = √100 = √(10^2 ) = 10 Distance MG Here, M (–3, –4) and G (6, 8) So, MG = √((𝟔−(−𝟑) )^𝟐+(𝟖−(−𝟒) )^𝟐 ) = √(〖(6+3)〗^2 + 〖(8+4)〗^2 ) = √(𝟗^𝟐+〖𝟏𝟐〗^𝟐 ) = √(81+144) = √225 = √(15^2 ) = 15 Thus, AM = 5, AG = 10 and MG = 15 Since MG = AG + AM Thus, all 3 points are collinear, i.e. they are on the same straight line