NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2 (2026-27)

1. 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 the figure, answer the given questions.

Question 1. 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?

Solution: Label the three given feet as A (8, 9), B (11, 9) and C (11, 7). In a rectangle, opposite sides are parallel to the axes here, so the missing corner D must line up vertically with A and horizontally with C. This means D takes its x-coordinate from A (which is 8) and its y-coordinate from C (which is 7). Hence, the fourth foot of the table is at D = (8, 7).

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

Solution: Yes, this position works well for the table. It sits fully inside the room without crossing any boundary, stays clear of the door's swing and the walking space, and its position close to the right wall keeps the centre of the room free, making it a convenient study corner.

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

Solution: Length of the table = difference of the x-coordinates of A (8, 9) and B (11, 9) = 11 − 8 = 3 units. Width of the table = difference of the y-coordinates of B (11, 9) and C (11, 7) = 9 − 7 = 2 units. The height cannot be found from the figure. The coordinate plane shows only the top view of the room in two dimensions, and height is a third dimension that a 2D figure does not capture.

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: The bathroom door runs from B₁ (0, 1.5) to B₂ (0, 4), so its width = 4 − 1.5 = 2.5 units. When the door swings open into the bedroom with its hinge fixed at B₁, the free end traces an arc of radius 2.5 units around B₁. The wardrobe stands along the line x = 3, between the points (3, 0) and (3, 2). The closest the wardrobe gets to the hinge B₁ (0, 1.5) is 3 units — which is more than the door's reach of 2.5 units. Since the arc never extends as far as the wardrobe, the door will not hit it.

If a wider door is planned, its swing radius would increase and could reach the wardrobe. Two simple adjustments would solve this: make the door open inward into the bathroom instead, or move the wardrobe slightly further to the right.

Question 3. Look at Reiaan's bathroom.

(i) What are the coordinates of the four corners O, F, R, and P of the bathroom?

Solution: Reading from the figure, the bathroom's four corners are: 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.

Solution: In SHWR, exactly one pair of opposite sides is parallel to each other, which makes the showering area a trapezium. Its corners are at: S = (−6, 6), H = (−3, 6), W = (−2, 9), R = (−6, 9)

(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.

Solution: Placing the washbasin space (3 ft wide, 2 ft deep) in the lower portion of the bathroom, its corners are: L = (−6, 2), M = (−3, 2), N = (−3, 0), P = (−6, 0)

Placing the toilet space (2 ft wide, 3 ft deep) just above it, its corners are: I = (−6, 5), J = (−4, 5), K = (−4, 2), L = (−6, 2)

Question 4. Other rooms in the house:

(i) Reiaan's room door leads from the dining room, which has a length of 18 ft and width of 15 ft. The dining room extends from point P to point A. Sketch the dining room and mark the coordinates of its corners.

Solution: P is at (−6, 0) and A is at (12, 0). Distance PA = 12 − (−6) = 18 ft ✓ — this matches the given length of the dining room. The dining room lies below the line PA, extending 15 units downward (its width). So PA forms the top edge, and the bottom edge lies along y = −15. The dining room PAUV therefore has corners: P = (−6, 0), A = (12, 0), U = (12, −15), V = (−6, −15)

(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.

Solution: First, find the centre of the dining room. x-coordinate of centre = (−6 + 12)/2 = 3 y-coordinate of centre = (0 + (−15))/2 = −7.5 So the centre is at (3, −7.5).

For a 5 ft × 3 ft table centred here, measure 2.5 ft (half the length) on either side along x, and 1.5 ft (half the width) on either side along y. The four feet of the table are at: E = (3 − 2.5, −7.5 − 1.5) = (0.5, −9) F = (3 + 2.5, −7.5 − 1.5) = (5.5, −9) G = (3 + 2.5, −7.5 + 1.5) = (5.5, −6) H = (3 − 2.5, −7.5 + 1.5) = (0.5, −6)

Think and Reflect (NCERT Textbook Page No. 9)

Question 1.
In moving from A (3, 4) to D (7, 1), what distance has been covered along the x-axis? What about the distance along the y-axis?

Solution:
From A (3, 4) to D (7, 1), the change along the x-axis is 7 - 3 = 4 units. The change along the y-axis is 4 - 1 = 3 units. So, the distance covered along the x-axis is 4 units and along the y-axis is 3 units.

Question 2.
Can these distances help you find the distance AD?

Solution:
Yes. The horizontal and vertical distances form a right triangle. So, using the Pythagorean theorem, AD = √(4² + 3²) = √25 = 5 units.

Think and Reflect (NCERT Textbook Page No. 11)

Question 1.
What has remained the same and what has changed with this reflection?

Solution:
After reflection, the lengths of the corresponding sides remain unchanged. However, the signs of the x-coordinates of the vertices change.

Question 2.
Would these observations be the same if ΔADM is reflected in the x-axis (instead of the y-axis)?

Solution:
No. If ΔADM is reflected in the x-axis, the signs of the y-coordinates will change, while the x-coordinates will remain the same.

Key Points from Vedantu’s Class 9 Maths Chapter 1 Exercise 1.2

• Locate points: Read and identify positions using ordered pairs.

• Find missing points: Use the given coordinates to determine unknown corners of shapes.

• Measure using coordinates: Calculate lengths and widths by comparing coordinate values.

• Apply coordinates in practical situations: Use graphs to represent rooms, furniture, and other layouts.

• Find distances: Work out horizontal, vertical, and actual distances between points.

• Understand reflections: Observe how coordinates change when a figure is reflected across the x-axis or y-axis.

Access Exercise-wise NCERT Solutions for Chapter 1 Maths Class 9

CBSE Class 9 Maths Chapter 1 Orienting Yourself: The Use of Coordinates Other Study Materials

Additional Study Materials for Class 9 Maths