Question 4 - End-of-Chapter Exercises - Chapter 1 Class 9 - Orienting Yourself: The Use of Coordinates (Ganita

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Question 4 Plot point Z (5, – 6) on the Cartesian plane. Construct a right-angled triangle IZN and find the lengths of the three sides. (Comment: Answers may differ from person to person.) We follow this process We plot point Z (5, –6) We now draw two lines – one vertical from point Z and one horizonal Let’s assume vertical point is 4 units above Z And horizontal point is 3 units on the left side of Z Let’s do this Now, our points are Z (5, –6), X (2, –6) and Y (5, –2) We already know XZ = 3 units, and YZ = 4 units But, let’s find all 3 lengths XZ, YZ, XY using Distance formula For XY Here, X (2, –6) and Y (5, –2) So, XY = √((𝟓−𝟐)^𝟐+(−𝟐−(−𝟔))^𝟐 ) = √(3^2+〖(−2+6)〗^2 ) = √(𝟑^𝟐+𝟒^𝟐 ) = √(9+16) = √25 = √(5^2 ) = 5 For XZ Here, X (2, –6) and Z (5, –6) So, XZ = √((𝟓−𝟐)^𝟐+(−𝟔−(−𝟔))^𝟐 ) = √(3^2+〖(−6+6)〗^2 ) = √(𝟑^𝟐+𝟎^𝟐 ) = √(3^2+0) = √(3^2 ) = 3 For YZ Here, Y (5, –2) and Z (5, –6) So, YZ = √((𝟓−𝟓)^𝟐+(−𝟔−(−𝟐))^𝟐 ) = √(0^2+〖(−6+2)〗^2 ) = √(𝟎+〖(−𝟒)〗^𝟐 ) = √(4^2 ) = 4