Coordinate Geometry (Chapter 1) CBSE Class 9 Ganita Manjari | NCERT Solutions

📐 Coordinate Geometry (Chapter 1) CBSE Class 9

Ganita Manjari | Complete Solutions with Detailed Explanation

📘 Exercise Set 1.1 (Based on Fig. 1.3)

Q1 Fig. 1.3 shows Reiaan’s room with points OABC marking its corners.
The x- and y-axes are marked in the figure.
Point O is the origin.
Referring to Fig. 1.3, answer the following questions:

Q1(i) If D1R1 represents the door to Reiaan’s room, how far is the door from the left wall (the y-axis) of the room? How far is the door from the x-axis?

✅ Detailed Explanation: The door lies on the x-axis (horizontal line).
Distance from x-axis = 0 (since on axis).
From figure, D₁ = (8,0).
Distance from y-axis = x-coordinate = 8 units.
Left wall is the y-axis.

Q1(ii) What are the coordinates of D1?

Answer: D₁ = (8, 0).
It is 8 units right of origin on x-axis.

Q1(iii) If R1 is the point (11.5, 0), how wide is the door? Do you think this is a comfortable width for the room door? If a person in a wheelchair wants to enter the room, will he/she be able to do so easily?

Explanation: Width = |11.5 – 8| = 3.5 units.
Assuming 1 unit = 1 ft → 3.5 ft = 42 inches.
Standard room door: 30–36 inches.
42" is wider than average → comfortable.
Wheelchair needs ≥32 inches (≈2.7 ft).
Since 3.5 > 2.7,
yes, wheelchair accessible easily.

Q1(iv) If B1 (0, 1.5) and B2 (0, 4) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?

Solution: Bathroom width = 4 – 1.5 = 2.5 units.
Room door = 3.5 units.
2.5 is less than 3.5 → bathroom door is narrower

💭 Think and Reflect (Real-world Observation)

🔍 Question 1: What are the standard widths for a room door? Look around your home and in school.

✅ Detailed Answer:

Location	Typical Width	Notes
Home (internal rooms)	30–36 inches (2.5–3 ft)	Common in Indian homes
Home (main entrance)	36–42 inches (3–3.5 ft)	Wider for furniture movement
School (classroom)	36–48 inches (3–4 ft)	Must accommodate student flow
School (office/staff)	30–36 inches (2.5–3 ft)	Standard internal door
International Standard (Wheelchair)	32 inches (≈2.7 ft) minimum	ADA / Accessibility guidelines

Conclusion: Standard room doors in Indian homes are typically 30–36 inches.
School doors are often wider at 36–48 inches.
International accessibility standards recommend a minimum of 32 inches clear width for wheelchair passage.

♿ Question 2: Are the doors in your school suitable for people in wheelchairs?

✅ Detailed Answer:

This depends on the specific school. Many modern schools in India now follow accessibility norms under the Rights of Persons with Disabilities Act (RPWD) 2016 and CBSE inclusive education guidelines.

✅ Suitable features (good schools):

• Door width ≥ 32 inches (2.7 ft) – allows wheelchair passage
• Ramps instead of steps at entrances
• Door handles at accessible height (not too high)
• Lightweight doors or automatic openers
• Thresholds that are flat or have small ramps

⚠️ Challenges in older schools:

• Doors may be only 24–28 inches wide – too narrow for wheelchairs
• Steps at entrance without ramps
• Heavy wooden doors difficult to open from a wheelchair
• Door handles placed too high

📌 Conclusion: While accessibility is improving across India, not all school doors are currently wheelchair suitable.
Students should observe their own school and suggest improvements if needed.

✍️ Exercise Set 1.2 (Study table, bathroom, dining room)

Q1 On a graph sheet, mark the x-axis and y-axis and the origin O.
Mark points from (– 7, 0) to (13, 0) on the x-axis and from (0, – 15) to (0, 12) on the y-axis.
(Use the scale 1 cm = 1 unit.)
Using Fig. 1.5, answer the given questions

1(i) Place Reiaan’s rectangular study table with three of its feet at the points (8, 9), (11, 9) and (11, 7). (i)Where will the fourth foot of the table be?

Reason: Rectangle: x-coordinate same as A(8) and y same as C(7) → (8,7).

1(ii) (ii) Is this a good spot for the table?

Answer: Yes, placed against the wall, does not block movement.

1(iii) What is the width of the table? The length? Can you make out the height of the table?

Width = 11-8 = 3 units; Length = 9-7 = 2 units. Height cannot be known (2D top view only).

2 If the bathroom door has a hinge at B1 and opens into the bedroom, will it hit the wardrobe? Are there any changes you would suggest if the door is made wider?

Door width = 2.5 units. Wardrobe starts at x=3 (>2.5) → will not hit. If made wider, shift wardrobe or make door open inward.

3(i) Look at Reiaan’s bathroom. (i) What are the coordinates of the four corners O, F, R, and P of the bathroom?

From Fig 1.5: O(0,9), F(0,0), R(-6,9), P(-6,0).

3(ii) (ii) What is the shape of the showering area SHWR in Reiaan’s bathroom? Write the coordinates of the four corners.

Shape = Trapezium. S(-6,5), H(-3,5), W(-2,9), R(-6,9).

3(iii) (iii) Mark off a 3 ft × 2 ft space for the washbasin and a 2 ft × 3 ft space for the toilet. Write the coordinates of the corners of these spaces.

Washbasin: (-6,0), (-3,0), (-3,2), (-6,2). Toilet: (-6,2), (-4,2), (-4,5), (-6,5).

4(i) 4. Other rooms in the house: (i) Reiaan’s room door leads from the dining room which has the length 18 ft and width 15 ft. The length of the dining room extends from point P to point A. Sketch the dining room and mark the coordinates of its corners.

P(-6,0), A(12,0), Q(12,-15), S(-6,-15).

4(ii) (ii) Place a rectangular 5 ft × 3 ft dining table precisely in the centre of the dining room. Write down the coordinates of the feet of the table.

Centre (3, -7.5). Feet: (0.5,-9), (5.5,-9), (5.5,-6), (0.5,-6).

🧠 In-text "Think and Reflect" (Detailed Answers)

1. What is the x-coordinate of a point on the y-axis?

Answer: Always 0. Example: (0,5), (0,-3).

2. Similar generalisation for a point on the x-axis?

y-coordinate = 0. Example: (4,0).

3. Does Q(y,x) ever coincide with P(x,y)?

Yes if and only if x = y. Coordinates are ordered pairs; order matters unless values equal.

4. If x≠y, then (x,y)≠(y,x) – true?

True. Example: (2,3) ≠ (3,2).

5. From A(3,4) to D(7,1): distance along x and y axes?

Δx = 4, Δy = 3. Then AD = √(4²+3²)=5 units (Baudhayana-Pythagoras).

6. Reflection across y-axis: what changes?

x-coordinate changes sign; y-coordinate same; distances and side lengths remain unchanged.

7. Would observations be same if reflected in x-axis?

Yes, but y-coordinate changes sign instead. Lengths preserved.

📌 End-of-Chapter Exercises (Full Solutions)

1. Intersection of x-axis and y-axis?

Origin (0,0).

2. W has x=-5. H on line through W ∥ y-axis. Coordinates? Quadrants?

H = (-5, y). QII if y>0, QIII if y<0, on axis if y=0.

3. R(3,0), A(0,-2), M(-5,-2), P(-5,2). Perpendicular sides? Parallel? Mirror?

Perpendicular: AM ⟂ MP. Parallel to axis: AM ∥ x-axis. Mirror: M and P about x-axis.

4. Plot Z(5,-6). Construct right triangle IZN. Lengths?

(Activity) Example: I(5,0) → IZ=6, ZN depends on N. Students verify.

5. System without negative numbers?

Only Quadrant I and positive axes. Cannot locate QII, QIII, QIV.

6. Collinearity M(-3,-4), A(0,0), G(6,8).

MA=5, AG=10, MG=15 → MA+AG=MG → collinear.

7. Collinearity R(-5,-1), B(-2,-5), C(4,-12).

RB=5, BC=√85≈9.22, RC=√202≈14.21 → 5+9.22≠14.21 → not collinear.

8(i) Right isosceles with origin as vertex.

O(0,0), A(4,0), B(0,4).

8(ii) Isosceles triangle: one vertex QIII, other QIV.

O(0,0), P(-3,-4), Q(3,-4). OP=OQ=5.

9. Midpoint table (S,M,T).

(-3,0)(0,0)(3,0)→Yes; (2,3)(3,4)(4,5)→Yes; (0,0)(0,5)(0,-10)→No; (-8,7)(0,-2)(6,-3)→No.

10. M(-7,1) midpoint of A(3,-4) and B(x,y). Find B.

x = -17, y = 6 → B(-17,6).

11. Trisection of A(4,7), B(16,-2): P (near A), Q.

P(8,4), Q(12,1).

12. Circle K centre O(0,0), A(1,-8), B(-4,7), C(-7,-4). Radius? D,E inside/outside?

Radius = √65 ≈8.06. D(-5,6): √61 < √65 → inside. E(0,9): 9 > √65 → outside.

13. Midpoints D(5,1),E(6,5),F(0,3) of ΔABC. Find A,B,C.

A(1,-1), B(11,3), C(-5,7).

14. City grid: intersections (4,3) and (3,4)?

Both refer to exactly 1 unique crossing each.

15. Computer screen 800×600. Circles A(100,150) r=80; B(250,230) r=100. Outside? Intersect?

Both circles fully inside (check edges). Distance AB = 170; sum radii =180 → 170<180 → intersect.

16. A(2,1), B(-1,2), C(-2,-1), D(1,-2). Square? Area?

All sides = √10, diagonals = √20 → square. Area = 10 sq units.

📖 Chapter Summary (as per Ganita Manjari)

• Two perpendicular lines: x-axis (horizontal) and y-axis (vertical).
• Origin = (0,0). Quadrants: I(+,+), II(-,+), III(-,-), IV(+,-).
• Distance formula: √[(x₂−x₁)² + (y₂−y₁)²] (Baudhayana-Pythagoras).
• Midpoint formula: ((x₁+x₂)/2 , (y₁+y₂)/2).
• If x=y then (x,y)=(y,x); otherwise ordered pair matters.

✅ All Intext Questions + Exercise 1.1 + Exercise Set 1.2 + Q1 to Q16 solved with reasoning.
📚 Based on NCERT CBSE Class 9 Ganita Manjari – Chapter 1: Orienting Yourself (The Use of Coordinates).
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