π Coordinate Geometry (Chapter 1) CBSE Class 9
Ganita Manjari | Complete Solutions with Detailed Explanation
π 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:
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, how far is the door from the left wall (y-axis)?
Fig. 1.1: Sketch of Reiaan’s room How far from x-axis?
Fig. 1.1: Sketch of Reiaan’s room How far from 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.
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.
It is 8 units right of origin on x-axis.
Q1(iii) R₁ = (11.5, 0). How wide is door?
Comfortable for wheelchair?
Comfortable for wheelchair?
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.
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) B₁(0,1.5), B₂(0,4). Bathroom door narrower or wider than room door?
Solution: Bathroom width = 4 – 1.5 = 2.5 units.
Room door = 3.5 units.
2.5 < 3.5 → bathroom door is narrower >
Room door = 3.5 units.
2.5 < 3.5 → bathroom door is narrower >
π Think and Reflect (Real-world Observation)
π 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
π 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)
1(i) Table feet: (8,9),(11,9),(11,7). Fourth foot?
Reason: Rectangle: x-coordinate same as A(8) and y same as C(7) → (8,7).
1(ii) Good spot for table?
Answer: Yes, placed against the wall, does not block movement.
1(iii) Width, length, height?
Width = 11-8 = 3 units; Length = 9-7 = 2 units. Height cannot be known (2D top view only).
2 Bathroom door hinged at B₁, opens into bedroom. Hits wardrobe? Suggestions if 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) Coordinates of bathroom corners O,F,R,P.
From Fig 1.5: O(0,9), F(0,0), R(-6,9), P(-6,0).
3(ii) Shape of SHWR? Coordinates.
Shape = Trapezium. S(-6,5), H(-3,5), W(-2,9), R(-6,9).
3(iii) Washbasin (3×2) & Toilet (2×3) coordinates.
Washbasin: (-6,0), (-3,0), (-3,2), (-6,2). Toilet: (-6,2), (-4,2), (-4,5), (-6,5).
4(i) Dining room corners (length 18ft, width 15ft, from P to A).
P(-6,0), A(12,0), Q(12,-15), S(-6,-15).
4(ii) 5×3 dining table centered. Feet coordinates.
Centre (3, -7.5). Feet: (0.5,-9), (5.5,-9), (5.5,-6), (0.5,-6).
π§ 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?
Ξx = 4, Ξy = 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.
π 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 ΞABC. 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.
π 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.
