source: ncert_exercises
topic: geometry
class_level: class_9
chapter: ch3
exercise: ex3.1
difficulty: beginner
Class 9 | Ch3: Coordinate Geometry | Exercise 3.1
Key concepts:
- Cartesian plane: two perpendicular number lines (x-axis horizontal, y-axis vertical)
- Origin O: point where axes intersect, coordinates (0,0)
- Ordered pair (x,y): x = abscissa (distance from y-axis), y = ordinate (distance from x-axis)
- Quadrant I (+,+), Quadrant II (-,+), Quadrant III (-,-), Quadrant IV (+,-)
Q1. How will you describe the position of a table lamp on your study table to another person? Answer: Consider the table as a plane and two perpendicular edges as axes. Measure perpendicular distance 'a' of the lamp from one edge (y-axis) and distance 'b' from the other edge (x-axis). Position of lamp = ordered pair (a, b). ✅
Q2. (Street Plan) A city has two main roads crossing at the centre (North-South and East-West). 7 streets run parallel to each other along North-South, and 7 streets along East-West. Identify the positions of cross streets on a city map, taking crossing of 2 main roads as origin. Answer: Let NS road = y-axis, EW road = x-axis, crossing = origin O. Each cross street is an intersection of a NS street and EW street. Using positive for East/North and negative for West/South, each intersection has unique coordinates (x,y). For example, 2nd street East and 3rd street North = (2,3). ✅