Chapter 1 : Orienting Yourself: The Use of Coordinates Textbook question and answer

Class 9 Ganita Manjari CBSE New Syllabus

Page 5: Exercise Set 1.1 & Think and Reflect

Referring to Fig. 1.3, answer the following questions:

(i) If $D_1R_1$D1​R1​ 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?

Answer: The door starts at point $D_1$D1​, which is located at $x = 8$x=8 on the x-axis. The left wall is the y-axis $(x = 0)$(x=0). Therefore, the door is 8 units (feet) from the left wall. Because the door lies exactly on the x-axis, its distance from the x-axis is 0 units.

(ii) What are the coordinates of $D_1$D1​?

Answer: Since $D_1$D1​ is situated exactly on the x-axis at the 8-unit mark, its coordinates are $(8, 0)$(8,0).

(iii) If $R_1$R1​ is the point $(11.5, 0)$(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?

Answer: The width of the door is the distance from $D_1(8, 0)$D1​(8,0) to $R_1(11.5, 0)$R1​(11.5,0), which is$$11.5 – 8 = \textbf{3.5 feet}$$11.5−8=3.5 feet

This is indeed a very comfortable width. Standard wheelchairs are typically 24 to 27 inches wide (about 2 to 2.25 feet), so a 3.5-foot door provides more than enough clearance for easy access.

(iv) If $B_1 (0, 1.5)$B1​(0,1.5) and $B_2 (0, 4)$B2​(0,4) represent the ends of the bathroom door, is the bathroom door narrower or wider than the room door?

Answer: The width of the bathroom door is the distance between $B_1$B1​ and $B_2$B2​, which is$$4 – 1.5 = \textbf{2.5 feet}$$4−1.5=2.5 feet

Since the room door is 3.5 feet wide, the bathroom door is narrower.

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Think and Reflect:

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

Answer: Standard interior room doors are usually between 30 and 36 inches wide (2.5 to 3 feet).

Are the doors in your school suitable for people in wheelchairs?

Answer: Typically, yes. Modern accessibility guidelines (like the ADA) require doors to have a minimum clear width of 32 inches to comfortably accommodate wheelchairs.

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Page 7: Think and Reflect

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

Answer: The x-coordinate of any point on the y-axis is always $0$0.

Is there a similar generalisation for a point on the x-axis?

Answer: Yes, the y-coordinate of any point situated on the x-axis is always $0$0.

Does point $Q (y, x)$Q(y,x) ever coincide with point $P (x, y)$P(x,y)? Justify your answer.

Answer: They only coincide if $x = y$x=y. A coordinate pair $(x, y)$(x,y) represents a specific location where order matters. For example, the point $(2, 5)$(2,5) is in an entirely different location than $(5, 2)$(5,2). However, if the values are identical (e.g., $(3, 3)$(3,3)), swapping them doesn’t change the location.

If $x \neq y$x=y, then $(x, y) \neq (y, x)$(x,y)=(y,x); and $(x, y) = (y, x)$(x,y)=(y,x) if and only if $x = y$x=y. Is this claim true?

Answer: Yes, this claim is entirely mathematically accurate.

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Pages 7–8: Exercise Set 1.2

1. Place Reiaan’s rectangular study table with three of its feet at the points $(8, 9), (11, 9)$(8,9),(11,9) and $(11, 7)$(11,7).

(i) Where will the fourth foot of the table be?

Answer: To form a rectangle aligned with the axes, the points must share x and y coordinates. We have x-coordinates 8 and 11, and y-coordinates 7 and 9. The missing combination to complete the rectangle is $x = 8$x=8 and $y = 7$y=7. Thus, the fourth foot is at $(8, 7)$(8,7).

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

Answer: Looking at Fig 1.5, the rectangle from $x=8$x=8 to 11 and $y=7$y=7 to 9 is tucked in the upper right corner of the bedroom. It sits neatly out of the main walking path, making it a highly practical spot.

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

Answer:
Length:$$|11 – 8| = \textbf{3 ft}$$∣11−8∣=3 ft

Width:$$|9 – 7| = \textbf{2 ft}$$∣9−7∣=2 ft

You cannot determine the height from this 2-D floor plan.

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2. If the bathroom door has a hinge at $B_1$B1​ and opens into the bedroom, will it hit the wardrobe? Are there any changes you would suggest if the door is made wider?

Answer: The hinge is at $B_1(0, 1.5)$B1​(0,1.5) and the door width is $2.5\text{ ft}$2.5 ft. The wardrobe’s closest corner is at $W_4(3, 2)$W4​(3,2). If the door swings open, it forms a quarter-circle with a radius of $2.5\text{ ft}$2.5 ft from $B_1$B1​.$$\text{Distance} = \sqrt{(3-0)^2 + (2-1.5)^2} = \sqrt{9 + 0.25} = \sqrt{9.25} \approx 3.04\text{ ft}$$Distance=(3−0)2+(2−1.5)2​=9+0.25​=9.25​≈3.04 ft

Since $3.04 > 2.5$3.04>2.5, the door will not hit the wardrobe. If the door were made wider (e.g., $3\text{ ft}$3 ft or more), the clearance would become uncomfortably tight or it would collide. A sliding door or having the door swing outward would be better alternatives.

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3. Look at Reiaan’s bathroom.

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

Answer: Based on the map in Fig 1.5 and the dimensions $(6\text{ ft} \times 9\text{ ft})$(6 ft×9 ft), the coordinates are:$$O(0, 0), \quad F(0, 9), \quad R(-6, 9), \quad P(-6, 0)$$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.

Answer: It is a square. The coordinates are$$S(-6, 6), \quad H(-3, 6), \quad W(-3, 9), \quad R(-6, 9)$$S(−6,6),H(−3,6),W(−3,9),R(−6,9)

It spans exactly $3\text{ ft} \times 3\text{ ft}$3 ft×3 ft.

(iii) Mark off a $3\text{ ft} \times 2\text{ ft}$3 ft×2 ft space for the washbasin and a $2\text{ ft} \times 3\text{ ft}$2 ft×3 ft space for the toilet.

Answer:
Washbasin: $(0, 9), (-3, 9), (-3, 7), (0, 7)$(0,9),(−3,9),(−3,7),(0,7)
Toilet: $(-6, 0), (-4, 0), (-4, 3), (-6, 3)$(−6,0),(−4,0),(−4,3),(−6,3)

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4. Other rooms in the house:

(i)

Answer:$$(-6, 0), \quad (12, 0), \quad (12, -15), \quad (-6, -15)$$(−6,0),(12,0),(12,−15),(−6,−15)

(ii)

Answer:
Center:$$x = \frac{-6 + 12}{2} = 3, \quad y = \frac{0 – 15}{2} = -7.5$$x=2−6+12​=3,y=20−15​=−7.5

Feet coordinates:$$(0.5, -6), \quad (5.5, -6), \quad (5.5, -9), \quad (0.5, -9)$$(0.5,−6),(5.5,−6),(5.5,−9),(0.5,−9)

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Page 9: Think and Reflect$$|7 – 3| = \textbf{4 units}$$∣7−3∣=4 units $$|1 – 4| = |-3| = \textbf{3 units}$$∣1−4∣=∣−3∣=3 units $$AD = \sqrt{4^2 + 3^2} = \sqrt{25} = \textbf{5 units}$$AD=42+32​=25​=5 units

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Page 11: Think and Reflect

Answer: The side lengths and y-coordinates remain the same. The x-coordinates change signs.

Answer: The x-coordinates remain the same, and the y-coordinates change signs.

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Pages 12–14: End-of-Chapter Exercises

1.What are the x-coordinate and y-coordinate of the point of intersection of the two axes?

Answer:- $$(0, 0)$$

2.Point W has x-coordinate equal to – 5. Can you predict the coordinates of point H which is on the line through W parallel to the y-axis? Which quadrants can H lie in?

Answer:- Answer: Because the line is parallel to the y-axis, all points on it share the exact same x-coordinate. So, the coordinates of H are (-5, y), where y can be any real number. Depending on the value of $y$, point H can lie in Quadrant II (if $y > 0$) or Quadrant III (if $y < 0$).

$$(-5, y)$$

3.
(i) AM and MP
(ii) AM
(iii) M and P (x-axis)

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4.$$ZI = 6,\quad IN = 5,\quad ZN = \sqrt{61}$$ZI=6,IN=5,ZN=61​

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5.
Restricted to first quadrant only.

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6.$$\frac{4}{3}, \quad \frac{4}{3}$$34​,34​

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7.$$\frac{-4}{3} \neq \frac{-7}{6}$$3−4​=6−7​

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8.
(i) $(0, 0), (5, 0), (0, 5)$(0,0),(5,0),(0,5)
(ii) $(0, 0), (-4, -5), (4, -5)$(0,0),(−4,−5),(4,−5)

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9.
Row 1: Yes
Row 2: Yes
Row 3: No
Row 4: No

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10.$$x = -17,\quad y = 6$$x=−17,y=6

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11.$$P(8, 4), \quad Q(12, 1)$$P(8,4),Q(12,1)

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12. (i)$$OA = OB = OC = \sqrt{65}$$OA=OB=OC=65​

(ii)$$OD = \sqrt{61}, \quad OE = 9$$OD=61​,OE=9

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13.$$(-1, -1), \quad (11, 3), \quad (1, 7)$$(−1,−1),(11,3),(1,7)

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14.
(i) 1
(ii) 1

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15.
(i) Inside screen
(ii) Intersect (170 < 180)

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16.$$\text{Side} = \sqrt{10}, \quad \text{Area} = 10$$Side=10​,Area=10