Question 3 - End-of-Chapter Exercises - Chapter 1 Class 9 - Orienting Yourself: The Use of Coordinates (Ganita

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Question 3 Consider the points R (3, 0), A (0, – 2), M (– 5, – 2) and P (– 5, 2). If they are joined in the same order, predict: (i) Two sides of RAMP that are perpendicular to each other. (ii) One side of RAMP that is parallel to one of the axes. (iii) Two points that are mirror images of each other in one axis. Which axis will this be? Now plot the points and verify your predictions. So, lets’ do it without plotting, and one by one (i) Two sides of RAMP that are perpendicular to each other. Now, from our graph Look at P (-5, 2) and M (-5, -2). They have the same x-coordinate, forming a perfectly vertical line. Look at M (-5, -2) and A (0, -2). They have the same y-coordinate, forming a perfectly horizontal line. Thus, sides PM and MA meet at a 90-degree angle and are perpendicular. Look at M (-5, -2) and A (0, -2). They have the same y-coordinate, forming a perfectly horizontal line. Thus, sides PM and MA meet at a 90-degree angle and are perpendicular. (ii) One side of RAMP that is parallel to one of the axes. Our points are R (3, 0), A (0, – 2), M (– 5, – 2) and P (– 5, 2) – joined in order From part (i), we saw that Side PM is a vertical line. So, it is parallel to the y-axis Side MA is a horizontal line. So, it is parallel to the x-axis (iii) Two points that are mirror images of each other in one axis. Which axis will this be? Our points are R (3, 0), A (0, – 2), M (– 5, – 2) and P (– 5, 2) – joined in order Mirror images of points would be those points with Same x-coordinate, y-coordinates flipped Or same y-coordinate, x-coordinates flipped Points P (-5, 2) and M (-5, -2) are mirror images. Since their x-coordinates are the same but their y-coordinates are flipped (positive vs. negative), they are mirror images across the x-axis. Our points are R (3, 0), A (0, – 2), M (– 5, – 2) and P (– 5, 2) – joined in order Mirror images of points would be those points with Same x-coordinate, y-coordinates flipped Or same y-coordinate, x-coordinates flipped Points P (-5, 2) and M (-5, -2) are mirror images. Since their x-coordinates are the same but their y-coordinates are flipped (positive vs. negative), they are mirror images across the x-axis. Let’s confirm these answers from plotting the points in the graph Plotting the points R (3, 0), A (0, – 2), M (– 5, – 2) and P (– 5, 2) and joining them Thus, we confirm PM is vertical (parallel to y-axis), MA is horizontal (parallel to x-axiss) PM is perpendicular to MA Points P & M are mirror images across x-axis