1. Orienting Yourself: The Use of Coordinates

6 topics56 min

Chapter 1 of NCERT Mathematics for Class 9: Orienting Yourself: The Use of Coordinates. Three sections — Why coordinates, The Cartesian plane and Distance in the plane. Six videos, 56 min in all.

Worked answers to the 21 exercise questions in this chapter →

0 of 6 done — sign in to track this chapter

Part 1

Why coordinates

10 minWhere coordinates came from: grid cities, meridians, and the road to the Cartesian planePoint across the room and say “it’s over there”. Say it down a telephone instead and you have just discovered why coordinates had to be invented.10 min · 13 partsहिंदी9 minDescribing a room you cannot see: a grid as a shared language for positionA loop of wool round a wardrobe hands over its shape exactly. Try to hand over where it stands and you cannot — position needs something shape does not.9 min · 13 partsहिंदी

Part 2

The Cartesian plane

10 minTwo axes, an origin, and why the order of the pair mattersOne number gives every point on a line its own address. Lift your finger off the floor and one number stops being enough.10 min · 12 partsहिंदी9 minThe four quadrants, and reading a point's signs off its positionTwo crossed lines do exactly one thing to the plane: they cut it. Ask any point which side it is on, twice, and you have read off its signs.9 min · 12 partsहिंदी

Part 3

Distance in the plane

9 minDistance when the segment is parallel to an axisThe easiest distance there is, usually waved through in a sentence. It gets an explanation because every right triangle in the general formula is built from two of them.9 min · 11 partsहिंदी9 minThe distance formula: Baudhāyana–Pythagoras rewritten in coordinatesThe distance formula is not a new fact. It is Baudhāyana–Pythagoras with the two legs written as coordinate differences.9 min · 12 partsहिंदी

What you will be able to do

  • State what a coordinate system must supply before any position can be named: two perpendicular reference directions, an origin, a unit, and signed numbers
  • State the difference between the shape of an object and its position, and say which of the two a wool outline can carry on its own
  • Construct a pair of axes: two perpendicular lines, equal units marked on both, the intersection named O
  • Name the plane and its axes using the chapter's three printed names for it
  • Recognise from a pair of coordinates alone whether a segment is parallel to an axis, lies on an axis, or is slanted
  • Given two points, construct the third vertex that makes a right triangle with legs parallel to the axes, and give its coordinates

What this chapter assumes you already know

  • The number line, including negative numbers to the left of zero, as met in the earlier classes' work on integers, rational numbers and decimals
  • That two lines can meet at a right angle, and what "perpendicular" means
  • Reading a simple map or plan, and the idea of a scale
  • The Baudhāyana–Pythagoras Theorem as a statement about a right triangle (studied in Class 8; used later in this chapter, at §1.4)
  • Directions on the ground: North, South, East, West
  • Reading a plan or map drawn to scale, and converting between model and reality
  • Measuring in feet, and the meaning of a written dimension such as 12 ft × 10 ft
  • Area of a rectangle, for the floor-space arithmetic

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "Descartes invented coordinates."
  • "The history is decoration in front of the real chapter."
  • "Grid streets are just tidy planning."
  • "Any two lines will do as axes."
  • "Zero and the negatives are just extra numbers."
  • "An origin is a natural feature of the world."
  • "A map shows you where things are, full stop."
  • "The wool outlines already tell Reiaan where the wardrobe is."