Exercise 1.2 Class 9 Maths Solutions | Ganita Manjari
Welcome to Sid Classes, your trusted destination for comprehensive academic resources! In this detailed study guide, we present complete, step-by-step solutions for the NCERT Class 9 Maths Ganita Manjari Chapter 1 Exercise 1.2. Designed to reflect how top-scoring students write their answers in school examinations, this walkthrough makes coordinate geometry, Cartesian plotting, and spatial reasoning entirely clear.
🔑 Key Concepts Used in this Exercise:
- Cartesian Coordinates: Representing real-world layouts, rooms, and furniture positions using \((x, y)\) coordinate pairs on a graph sheet.
- Distance Formula & Dimensions: Determining lengths, widths, and structural placements by calculating coordinate differences along the axes.
- Geometric Shapes on Planes: Identifying squares, rectangles, and trapeziums based on coordinate points and parallel properties.
NCERT Class 9 Maths Ganita Manjari Chapter 1 Exercise 1.2 Solutions
Question 1
Place Reiaan’s rectangular study table with three of its feet at the points (8, 9), (11, 9) and (11, 7).
Solution:
(i) Where will the fourth foot of the table be?
Given three points are \((8, 9)\), \((11, 9)\), and \((11, 7)\).
Therefore, the fourth foot must lie at \(\mathbf{(8, 7)}\) to complete the rectangular shape.
(ii) Is this a good spot for the table?
Yes, this spot is ideal for a study table because:
- The table is positioned neatly near the wall.
- It does not obstruct or block any room doors.
(iii) What is the width of the table? The length? Can you make out the height of the table?
• Width of table: Distance between \((8, 9)\) and \((11, 9)\) \(\implies 11 - 8 = \mathbf{3}\) units.
• Length of table: Distance between \((11, 9)\) and \((11, 7)\) \(\implies 9 - 7 = \mathbf{2}\) units.
• Height of the table: No, the height cannot be determined from a 2D Cartesian coordinate plane since height lies along the vertical z-axis, which is not represented here.
Question 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?
Solution:
From Fig. 1.5:
• \(B_1 = (0, 1.5)\)
• \(B_2 = (0, 4)\)
The width of the bathroom door is: \(4 - 1.5 = 2.5\) units.
If the bathroom door opens towards the bedroom with \(B_1\) as the hinge point, the door swings in an arc of radius \(2.5\) units.
The wardrobe starts from coordinates \(W_1 = (3, 0)\) to \(W_4 = (3, 2)\). Since the wardrobe is more than \(2.5\) units away from the hinge point \(B_1\), the door will not touch the wardrobe while opening.
Suggested changes if the door is made wider:
• Shift the wardrobe slightly further away, or
• Design the door to open inward to optimize bedroom space.
Question 3
Look at Reiaan’s bathroom.
Solution:
(i) What are the coordinates of the four corners O, F, R, and P of the bathroom?
• \(O = (0, 0)\)
• \(F = (0, 9)\)
• \(R = (-6, 9)\)
• \(P = (-6, 0)\)
(ii) What is the shape of the showering area SHWR in Reiaan’s bathroom? Write the coordinates of the four corners.
Coordinates from Fig. 1.5:
• \(S = (-6, 5)\)
• \(H = (-3, 5)\)
• \(W = (-2, 9)\)
• \(R = (-6, 9)\)
Since points \(S\) and \(H\) lie on the horizontal line \(y = 5\), and points \(R\) and \(W\) lie on the horizontal line \(y = 9\), side \(SH\) is parallel to side \(RW\). Because one pair of opposite sides is parallel, quadrilateral \(SHWR\) is a trapezium.
(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 Space (3 ft × 2 ft):
Placed in the lower-left corner of the bathroom with coordinates:
\((-6, 0), (-3, 0), (-3, 2), (-6, 2)\)
Toilet Space (2 ft × 3 ft):
Placed just above the washbasin area with coordinates:
\((-6, 2), (-4, 2), (-4, 5), (-6, 5)\)
Question 4
Other rooms in the house:
Solution:
(i) Reiaan’s room door leads from the dining room which has 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.
PNMA represents the dining room layout.
(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.
Coordinates of the dining table feet are: \(\mathbf{(0.5, -6), (5.5, -6), (5.5, -9), (0.5, -9)}\).
Frequently Asked Questions (FAQs)
Q1: What is Exercise 1.2 Class 9 Maths about?
A: Exercise 1.2 of Class 9 Maths focuses on coordinate geometry and helps students understand plotting points and real-world spatial layouts on the Cartesian plane.
Q2: Are these Exercise 1.2 solutions based on the latest CBSE syllabus?
A: Yes, these solutions are prepared according to the latest CBSE syllabus and NCERT Ganita Manjari guidelines.
Q3: How can I solve coordinate geometry questions easily?
A: Students should practice plotting points regularly and understand the x-axis, y-axis, and coordinate differences clearly.
Q4: Can I use these solutions for exam preparation?
A: Yes, these step-by-step solutions are extremely useful for homework, revision, and CBSE school exam preparation.
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