Class 9 Maths Chapter 1 PPT (18 Slides) – Coordinate Geometry: Orienting Yourself | USP Indore

Class 9 Maths Chapter 1 PPT – Orienting Yourself: The Use of Coordinates | 18 Slides | USP Indore

Download the complete 18-slide illustrated PowerPoint presentation for Class 9 Maths Chapter 1 – Orienting Yourself: The Use of Coordinates, prepared by Unique Study Point (USP), Indore. This PPT is based on the NCERT Ganita Manjari (Grade 9, Part 1) syllabus (Session 2026-27) and covers every topic, activity, exercise, and real-life application of Coordinate Geometry in a visual and easy-to-understand format.

Complete Topic Coverage — 18 Slides

📘 Slide 1 — Chapter Overview (Topic List)

• What is a Coordinate System?
• History – India\'s Contribution to Coordinates
• The 2-D Cartesian Plane: x-axis, y-axis, Origin
• The Four Quadrants: I, II, III, IV
• Plotting Points on the Plane
• Distance Between Two Points
• Baudhāyana–Pythagoras Theorem in Coordinates

🏛️ Slide 2 — History of Coordinates: India\'s Contribution

• Sindhu-Sarasvati Civilisation (3000+ BCE): First real coordinate grid — counting N-S and E-W from the city centre
• Ujjayini as Zero Meridian (4th century BCE): Ancient India\'s Greenwich — all locations measured from Ujjayini; even Ptolemy mentioned it
• Baudhāyana (c. 800 BCE): Used E-W and N-S lines for geometry; proved the Baudhāyana-Pythagoras theorem — backbone of the distance formula
• Āryabhaṭa (c. 499 CE): Mapped the sky using coordinates; replaced chords with sines; made calculating star positions easier
• Brahmagupta (c. 628 CE): Formalised ZERO and NEGATIVE numbers — without these, the 4-quadrant plane is impossible!
• René Descartes (1637 CE): Final formalisation of 2-D coordinates — but built entirely on Indian mathematical foundations
• Knowledge chain: Brahmagupta\'s work → Arabic (\'Sindhind\') → Al-Bīrūnī → Europe (12th century) → Descartes 1637

🏠 Slide 3 — Mapping Reiaan\'s Room: Where Coordinates Begin!

• NCERT context activity: Reiaan maps his room on a coordinate grid using pins and threads
• Room layout: Bathroom (6 ft × 9 ft), Bedroom (12 ft × 10 ft), Wardrobe (4 ft × 2 ft)
• Scale: 1 cm = 1 foot; each pin = a point (x, y); threads show walls and furniture
• Think question: Why can\'t we show windows on this floor map? (Hint: Windows are on the WALLS, not the FLOOR!)
• Inclusive learning: A visually impaired student can FEEL the room with fingers using pins and threads

📐 Slide 4 — The 2-D Cartesian Coordinate System

• x-axis = Horizontal line (left ↔ right); Right of O → x is POSITIVE; Left of O → x is NEGATIVE
• y-axis = Vertical line (up ↕ down); Above O → y is POSITIVE; Below O → y is NEGATIVE
• Origin O = (0, 0) — where x-axis and y-axis intersect; starting point of ALL measurements
• Points on axes: B = (4.5, 0) on x-axis; H = (0, 4) on y-axis; E = (-2.9, 0); G = (0, -4.5)
• Key rule: x comes FIRST, then y — always write (x, y)!

🗺️ Slide 5 — The Four Quadrants: Signs of Coordinates

• Quadrant I (+x, +y): Both positive — example P(5, 4)
• Quadrant II (−x, +y): x negative, y positive — example Q(−5, 3)
• Quadrant III (−x, −y): Both negative — example R(−3, −4)
• Quadrant IV (+x, −y): x positive, y negative — example S(3, −5)
• Quick Memory Trick: I → Both + (happy place!) | II → x−, y+ (left but up!) | III → Both − (deep underground!) | IV → x+, y− (right but sinking!)
• Quadrants go ANTI-CLOCKWISE starting from Quadrant I

📍 Slides 6 & 7 — How to Plot a Point on the Cartesian Plane (4 Steps)

• Step 1: Start at the ORIGIN O (0, 0)
• Step 2: Move along x-axis by x units (positive → RIGHT, negative → LEFT)
• Step 3: From there, move parallel to y-axis by y units (positive → UP, negative → DOWN)
• Step 4: Mark the point and label it (x, y)
• Examples: P(5, 3) and Q(−4, −2) plotted step by step
• Reiaan\'s room corners mapped: O(0,0), A(12,0), B(12,10), C(0,10); Door: D₁(9,0) to R₁(11.5,0)
• REMEMBER: Always write x FIRST, then y → (x, y) NOT (y, x)! The order matters — (3,5) ≠ (5,3)!

📏 Slide 8 — Distance Between Two Points: Baudhāyana–Pythagoras Theorem

• Baudhāyana (c. 800 BCE): In a right triangle, (hypotenuse)² = (height)² + (base)² — the key to the distance formula!
• Distance Formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²]
• Example 1: Distance AD where A(3,4) and D(7,1): Horizontal shift = 4, Vertical shift = 3 → AD = √(16+9) = √25 = 5 units
• Example 2: DM where D(7,1) and M(9,6): DM = √(2²+5²) = √29 units
• Example 3: MA where M(9,6) and A(3,4): MA = √(6²+2²) = √40 = 2√10 units
• Tip: Even if (x₂−x₁) is negative, we SQUARE it → always positive! Distance is always ≥ 0.

🪞 Slide 9 — Reflection of Points: Negative Coordinates

• Reflection in y-axis rule: (x, y) → (−x, y); x becomes negative, y stays same
• A(3,4) → A\'(−3,4); D(7,1) → D\'(−7,1); M(9,6) → M\'(−9,6)
• Mirror line = y-axis (x = 0)
• Big Idea: Reflection PRESERVES distances! The shape stays exactly the same size — only its position changes. This is called CONGRUENCE.
• Verified: AD = A\'D\' = 5 units; DM = D\'M\' = √29 units; MA = M\'A\' = √40 units ✓

📋 Slide 10 — Key Concepts Summary: Coordinate Geometry Essentials

• Origin = O = (0,0); where x-axis and y-axis meet
• Points on x-axis → (x, 0); y-coordinate is ALWAYS 0. Examples: (5,0), (−3,0), (7.5,0)
• Points on y-axis → (0, y); x-coordinate is ALWAYS 0. Examples: (0,4), (0,−2), (0,7)
• Quadrant sign table: I(+,+); II(−,+); III(−,−); IV(+,−)
• (x,y) vs (y,x) — ORDER MATTERS: (3,5) ≠ (5,3); (x,y) = (y,x) ONLY if x = y
• Distance formula: d = √[(x₂−x₁)² + (y₂−y₁)²]; based on Baudhāyana–Pythagoras theorem
• India\'s contribution: Brahmagupta → zero + negative numbers → 4-quadrant plane; Baudhāyana → distance theorem; Āryabhaṭa → celestial coordinates

🏠 Slide 11 — Exercise Set 1.2: Reiaan\'s Room Fully Mapped

• Full room on coordinate plane: O(0,0) origin, A(12,0) corner A, B(12,10) corner B, C(0,10) corner C
• Bathroom door: B₁(0,1.5) and B₂(0,4); Room door: D₁(9,0) and R₁(11.5,0)
• Wardrobe: W₁(3,0), W₂(7,0), W₃(2), W₄(3,2); Study table corners: (8,7), (11,7), (8,9), (11,9)
• Q1: How far is door D₁ from the y-axis? What are coordinates of D₁?
• Q2: If R₁ = (11.5, 0), how wide is the room door? Can a wheelchair enter?
• Q3: Is bathroom door B₁B₂ wider or narrower than room door D₁R₁?

📐 Slide 12 — Distance Formula: Worked Examples and Practice

• Three full worked examples: AD where A(3,4) D(7,1); DM where D(7,1) M(9,6); MA where M(9,6) A(3,4)
• Practice problems: Distance between O(0,0) and Z(5,−6); P(1,−8) and Q(−4,7); R(−7,−4) and S(0,0)
• NCERT problems: Are M(−3,−4), A(0,0), G(6,8) collinear? (Check if MA + AG = MG)
• Show that A(1,−8), B(−4,7) and C(−7,−4) lie on a circle centred at O(0,0). Find the radius.

⭐ Slide 13 — Chapter 1 Summary Mind Map

• The Cartesian Plane: two perpendicular lines, 4 quadrants, origin (0,0)
• Plotting a point (x,y): 4-step method
• Coordinate Rules: axis points, quadrant signs, order matters
• Distance Formula: d = √[(x₂−x₁)² + (y₂−y₁)²] (Baudhāyana–Pythagoras)
• Reflection in y-axis: (x,y) → (−x,y); distances preserved; congruence
• Important Problems to try: RAMP shape, collinear points, circle, midpoint
• India\'s Gift: Sindhu-Sarasvati (3000+ BCE) → Baudhāyana (800 BCE) → Brahmagupta (628 CE) → Descartes (1637 CE)

📝 Slide 14 — Exercise Set 1.1: Reiaan\'s Room Questions

• Q1: If D₁R₁ represents the room door, how far is it from the left wall (y-axis)?
• Q2: What are the coordinates of D₁?
• Q3: If R₁ = (11.5, 0), how wide is the door D₁R₁? Can a wheelchair enter? (Standard width = 32 inches)
• Q4: Is bathroom door B₁B₂ wider or narrower than room door? Calculate using distance formula.
• Think and Reflect: What are standard widths for a room door? Are school doors suitable for wheelchair users?

🏡 Slide 15 — Exercise Set 1.2: Reiaan\'s Full House

• Q1 Study Table: Three feet at (8,9), (11,9), (11,7). Find fourth foot; find width and length of table.
• Q2 Bathroom Door Problem: If bathroom door has hinge at B₁(0,1.5) and opens INTO bedroom, will it hit wardrobe? What if door is wider?
• Q3 Bathroom Layout: Find coordinates of corners O, F, R, P; find shape and coordinates of showering area SHWR; mark spaces for washbasin and toilet.
• Q4 Dining Room and Table: Dining room from P(−6,0) to A(12,0), 18 ft long and 15 ft wide. Place a 5 ft × 3 ft table PRECISELY in the CENTRE.

📝 Slides 16, 17, 18 — End-of-Chapter Exercises (Q1 to Q16)

• Q1: x and y coordinates of the point of intersection of the two axes (Origin)
• Q2: Point W has x-coordinate = −5; predict coordinates of H on line through W parallel to y-axis; which quadrants can H lie in?
• Q3: Points R(3,0), A(0,−2), M(−5,−2), P(−5,2) — if joined in order R→A→M→P→R, predict: perpendicular sides, parallel side, mirror image points
• Q4: Plot Z(5,−6); construct right-angled triangle IZN; find lengths of three sides using distance formula
• Q5: What would a coordinate system be like WITHOUT negative numbers? Can we locate all points on a 2-D plane?
• Q6 ★: Are M(−3,−4), A(0,0), G(6,8) on the same straight line? Method: check if MA + AG = MG (collinearity)
• Q7 ★: Check if R(−5,−1), B(−2,−5), C(4,−12) are collinear — plot and verify
• Q8 ★: Using origin as vertex: (i) plot right-angled isosceles triangle; (ii) plot isosceles triangle with one vertex in Quadrant III and other in Quadrant IV
• Q9 ★: Midpoint table — check if M is midpoint of ST for 4 sets of points using midpoint formula: x of M = (x of S + x of T) ÷ 2
• Q10 ★: If M(−7,1) is midpoint of A(3,−4) and B(x,y), find B
• Q11 ★: Points of trisection P and Q of AB where A(4,7) and B(16,−2)
• Q12 ★: A(1,−8), B(−4,7), C(−7,−4) lie on circle K centred at O(0,0). Find radius; check if D(−5,6) and E(0,9) lie within, on, or outside circle
• Q13: City coordinate map — roads crossing at centre; 10 streets in each direction; how many crossings can be called (4,3)? And (3,4)?
• Q14: City coordinate model — 1 cm = 200 m; identify crossings
• Q15 ★: Computer screen 800 × 600 pixels; Circle A: centre (100,150) radius 80; Circle B: centre (250,230) radius 100. Does any part lie OUTSIDE screen? Do circles INTERSECT?
• Q16 ★: Plot A(2,1), B(−1,2), C(−2,−1), D(1,−2). Is ABCD a square? Find area.

Key Features of This Presentation

• ✅ 18 slides — complete NCERT Ganita Manjari Chapter 1 coverage
• ✅ India\'s rich history of coordinate geometry: Sindhu-Sarasvati, Baudhāyana, Āryabhaṭa, Brahmagupta
• ✅ NCERT context fully covered: Reiaan\'s Room mapping activity (Exercise Set 1.1 and 1.2)
• ✅ Distance formula derivation using Baudhāyana–Pythagoras theorem
• ✅ Reflection of points in y-axis with congruence concept
• ✅ All 16 end-of-chapter exercises (Q1 to Q16) covered across 3 slides
• ✅ Challenge questions (★) for collinearity, midpoint, circle, isosceles triangle
• ✅ Real-world applications: city maps, computer screens, wheelchair-accessible doors
• ✅ Mind Map summary slide for quick revision
• ✅ Prepared as per CBSE NCERT Ganita Manjari Class 9 Syllabus 2026-27

Important Formulas Covered

• Distance Formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²]
• Points on x-axis: (x, 0); Points on y-axis: (0, y)
• Reflection in y-axis: (x, y) → (−x, y)
• Midpoint of ST: x of M = (x of S + x of T) ÷ 2; y of M = (y of S + y of T) ÷ 2
• Quadrant signs: I(+,+); II(−,+); III(−,−); IV(+,−)
• Collinearity check: MA + AG = MG → points are collinear

Important FAQs — Class 9 Maths Coordinate Geometry

Q. What is the Cartesian plane?
Ans. The Cartesian plane is a 2-D surface formed by two perpendicular number lines — the horizontal x-axis and the vertical y-axis — intersecting at the origin O(0,0). It is divided into four quadrants and is used to represent points using ordered pairs (x, y).

Q. What is the distance formula in coordinate geometry?
Ans. The distance between two points (x₁, y₁) and (x₂, y₂) is d = √[(x₂ − x₁)² + (y₂ − y₁)²]. This formula is derived from the Baudhāyana–Pythagoras theorem applied to the horizontal and vertical shifts between the two points.

Q. What are the signs of coordinates in the four quadrants?
Ans. Quadrant I: (+, +); Quadrant II: (−, +); Quadrant III: (−, −); Quadrant IV: (+, −). The quadrants are numbered anti-clockwise starting from the top-right.

Q. What are the coordinates of any point on the x-axis?
Ans. Any point on the x-axis has its y-coordinate equal to 0. It is written as (x, 0). Examples: (5, 0), (−3, 0), (7.5, 0).

Q. What happens to coordinates when a point is reflected in the y-axis?
Ans. When a point (x, y) is reflected in the y-axis, the x-coordinate becomes negative while y stays the same. The reflected point is (−x, y). For example, A(3, 4) → A\'(−3, 4). Distances are preserved after reflection — the shape is congruent.

Q. How do you check if three points are collinear using the distance formula?
Ans. Three points M, A, G are collinear if MA + AG = MG (the sum of two smaller distances equals the largest). If this condition holds, the points lie on the same straight line. This can be verified using the distance formula for each pair of points.

Q. Who invented the coordinate system?
Ans. While René Descartes (1637 CE) is credited with formalising the 2-D Cartesian system, its foundations were laid by Indian mathematicians centuries earlier — Baudhāyana (800 BCE) proved the distance theorem, Brahmagupta (628 CE) formalised zero and negative numbers (essential for the 4-quadrant plane), and the Sindhu-Sarasvati Civilisation (3000+ BCE) used a coordinate-style city grid.

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