E ExamMaster

CBSE Class 9 · Mathematics

Orienting Yourself: The Use of Coordinates

Official NCERT chapter from Ganita Manjari Part I (book code iemh1). ExamMaster notes are original teaching at CBSE Class 9 depth.

This lesson follows the official chapter “Orienting Yourself: The Use of Coordinates” in Ganita Manjari Part I. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 9
  • Medium level
  • 8 concepts

1Settling In

Settling in means agreeing a pair of axes and an origin so a point can sit as (x, y). Without that agreement, “here” is a finger, not a record.

Two people pointing at a page without axes are not settled.

Figure. Before (x, y) has a formula, a seat already has two names: which column, which row. Ria sits in column 2, row 1 — a pair that locates one seat.

How it works

  1. Draw x across and y up, crossing at OThe agreement.
  2. Read right/up as positive unless told otherwiseThe signs.
  3. Write a point as an ordered pair(3, 2) is not (2, 3).

2The 2-d Cartesian Coordinate System

The 2-d Cartesian plane is the grid of those pairs. Quadrants are sign-regions: (+,+), (−,+), (−,−), (+,−). The axes themselves are not inside a quadrant.

A point on the y-axis is not in Quadrant I just because y is positive.

Figure. The plane is two number lines crossing at O. x is rightward, y is upward. Point (3, 2) is 3 along x and 2 along y.

How it works

  1. Read the signs of x and yThe region.
  2. Name the quadrant, or say “on an axis”The sort.
  3. Keep (0, 0) as the origin, not a quadrantO.

3Distance Between Two Points in the 2-D Plane

Distance between (x1, y1) and (x2, y2) is the hypotenuse of the right triangle whose legs are |x2−x1| and |y2−y1|: √[(x2−x1)² + (y2−y1)²]. A count of grid steps that ignores the diagonal is a walk, not this distance.

3 across and 4 up is 5, not 7.

Figure. Distance is the hypotenuse of the right triangle whose legs are Δx and Δy. Here Δx = 4, Δy = 3, so AB = 5.

How it works

  1. Subtract the xs and the ysThe legs.
  2. Square, add, square-rootThe hypotenuse.
  3. Keep the unit if the grid has oneThe distance.

3-4-5 on the plane

Distance from (1, 2) to (4, 6).

  • Δx3
  • Δy4
  • √(9+16)5

Pro tip. The plane-distance is the right-triangle hypotenuse.

4A definition is a test you can run

A coordinate pair is a test: two numbers in order from an agreed origin. If you cannot name the axes, you have a doodle.

A labelled city-map without x and y is a different locate.

Figure. The definition is a test you can run: form Δx and Δy, square, add, take the root. If the root is 5, the segment is 5 long on this equal-scale plane.

How it works

  1. Name origin and axesThe object.
  2. Write (x, y) in orderThe test.
  3. If the order swaps, it is a different pointThe definition ran.

5Name the given before the unknown

The given are the two points (or one point and the axes). The unknown is a quadrant or a distance. Copy the order (x, y) before you subtract.

Swapping 3 and 2 because the picture “looks taller” is a silent given.

Figure. Name the givens first: A(1, 2) and B(5, 5). The unknown is the length AB, not another point.

How it works

  1. Copy the pairsThe given.
  2. Name quadrant or distanceThe unknown.
  3. Then read signs or run the formulaGiven first.

6One worked case is enough at this class

One distance is enough. A page of (1,2) to (4,6) clones does not add a new hypotenuse.

Ten twins of 5 are still one idea.

Figure. One worked pair: A(4, 8), B(7, 9). Δx = 3, Δy = 1, so AB = √10. Leave the surd; 10 is not a square.

How it works

  1. Compute one distance or one quadrantThe case.
  2. A second only as a checkOptional.
  3. StopThis class.

7A miss: swapping the school name for the picture

A classroom-seating photo is a setting. The maths is (row, column) only after you agree which is x. Counting smiling faces and skipping the pair is the swap-miss.

A group photo is not the Cartesian plane.

Figure. The miss is swapping the names: (2, 5) is not the same seat as (5, 2). The first number is x, the second is y — the picture must match that order.

How it works

  1. Keep the photo as a storyA setting.
  2. Agree axes and write a pairThe maths.
  3. Then distance or quadrantDo not swap.

8Check by the opposite action or the opposite test

Check a distance by building the right triangle on the grid and using a known triple, or by swapping the two points — the distance must match. Check a quadrant by the signs alone.

Counting Manhattan blocks is not the opposite test for this formula.

Figure. The check is the opposite walk: B to A uses −Δx and −Δy, but the squares are the same, so |AB| = |BA|.

How it works

  1. State 5 or “Quadrant II”The claim.
  2. Rebuild legs or reread signsThe check.
  3. Mend if they disagreeHonest.
Distance from (1, 2) to (4, 6) is
  1. 5
  2. 7
  3. 3

√(3²+4²)=5, not 3+4.

Notes

  • The official chapter title is “Orienting Yourself: The Use of Coordinates”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • distance = √[(x2−x1)² + (y2−y1)²]

Recap

Hold these pegs from the official chapter “Orienting Yourself: The Use of Coordinates”. The wording is ExamMaster’s teaching, not a textbook recap.

Settling In
Settling in means agreeing a pair of axes and an origin so a point can sit as (x, y).
The 2-d Cartesian Coordinate System
The 2-d Cartesian plane is the grid of those pairs.
Distance Between Two Points in the 2-D Plane
Distance between (x1, y1) and (x2, y2) is the hypotenuse of the right triangle whose legs are |x2−x1| and |y2−y1|: √[(x2−x1)² + (y2−y1)²].
A definition is a test you can run
A coordinate pair is a test: two numbers in order from an agreed origin.
Name the given before the unknown
The given are the two points (or one point and the axes).
One worked case is enough at this class
One distance is enough. A page of (1,2) to (4,6) clones does not add a new hypotenuse.

Practise Orienting Yourself: The Use of Coordinates

Reading is free and needs no account. Practice, mocks and progress live in the app.

  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
Continue with Google — freeNo card, no trial. Works offline once installed.