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Coordinate Geometry — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsCoordinate Geometry4 Marks
Question
Read the Source/ Text given below and answer these questions:

Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was having tiles of four colours orange, yellow, green and blue. He fitted the tiles in 8 columns and 12 rows. The size of one tile was 1 foot × 1 foot and the area of each tile is 1 foot2. He arranged the tile in such a way that colour of tiles in each row and column were in the pattern: Orange → Yellow → green → Blue → Orange → ..... and so on. Now answer the following questions:
  1. Which colour tile was fitted at the point with coordinates (5, 3)?
  1. Orange.
  2. Yellow.
  3. Green.
  4. Blue.
  1. Which colour tile was fitted at the point with coordinates (7, 7)?
  1. Orange.
  2. Yellow.
  3. Green.
  4. Blue.
  1. Which colour tile was fitted at the point with coordinate (2, 5)?
  1. Orange.
  2. Yellow.
  3. Green.
  4. Blue.
  1. What is the area of the tiles fitted in the rectangular part OABX?
  1. 50 foot2
  2. 24 foot2
  3. 12 foot2
  4. 48 foot2
  1. What is the ordinate of top row tiles?
  1. 8
  2. 12
  3. 16
  4. 6
✓

Answer

(i)(c)Green.
(ii)(a)Orange.
(iii)(b)Yellow.
(iv)(d)48 foot2
(v)(b)12

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To beautify parks in a city, city municipal corporation decided to make triangular flower beds in parks as shown in Fig. The dimensions of a triangular flower bed are $75 m \times 80 m \times 85 m$. Based on this information answer the following questions:
Image
(i) If each triangular flower bed is to be fenced with two parallel wires one below the other than the length of the wire used is
(a) 120 m$\quad$(b) 240 m$\quad$(c) 260 m$\quad$(d) 480 m
(ii) The area of a flower bed is
(a) $300 \sqrt{42} m^2$$\quad$(b) $300 \sqrt{21} m^2$$\quad$(c) $600 \sqrt{21} m^2$$\quad$(d) $400 \sqrt{21} m^2$
(iii) If each triangular bed is an equilateral triangle of side 60 m, then its area is
(a) $900 \sqrt{3} m^2$$\quad$(b) $600 \sqrt{3} m^2$$\quad$(c) $1200 \sqrt{3} m^2$$\quad$(d) $400 \sqrt{3} m^2$
(iv) The area of an isosceles triangle with base 'a' and equal sides 'b' is given by
(a) $\frac{a}{4} \sqrt{4 b^2-a^2}$$\quad$(b) $\frac{b}{4} \sqrt{4 a^2-b^2}$$\quad$(c) $\frac{a}{2} \sqrt{2 b^2-a^2}$$\quad$(d) $\frac{b}{2} \sqrt{4 a^2-b^2}$
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Read the Source/ Text given below and answer these questions:

In an effort to provide high-quality and safe playgrounds for kids, our reputable manufacturers adhere to the playground safety guidelines set forth by the Indian Consumer Product Safety Commission (CPSC) and the Indian Society for Advancement of Materials and Processing Engineering (ISAMPE). These organizations set the guidelines for determining the types of playground equipment that is appropriate for kids within specific age groups: 2-3 years, 3-5 years, 5-7 years, 7-10 years, 10-15 years, and 15-17 years. A random survey of the number of children of various age groups playing in a park was found as follows:

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1-2
5
2-3
3
3-5
6
5-7
12
7-10
9
10-15
10
15-17
4
The histogram is as given below:

  1. In this question, the class sizes are different. So, calculate the adjusted frequency for each class by using the following formula:

Frequency density or adjusted frequency for class:

  1. $\frac{\text{Minimum class size}}{\text{Class size of this class}}\times\text{Its Frequency}$

  2. $\frac{\text{Minimum class mark}}{\text{Class size of this class}}\times\text{Its Frequency}$

  3. $\frac{\text{Minimum Frequency}}{\text{Class size of this class}}\times\text{Its class size}$

  4. $\frac{\text{Minimum class mark}}{\text{Class mark of this class}}$

  1. In this question the minimum class size is:
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  2. 1
  3. 2
  4. 3
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  2. Lower limit = 5, upper limit = 7
  3. Lower limit = 3, upper limit = 5
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  2. 3, 3
  3. 6, 6
  4. 6, 3
  1. Find the class mark of class 15 - 17:
  1. 16
  2. 12
  3. 25
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  1. SSS
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Image

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Image
5. What is the sum of the four marked angles?
  A. 180°
  B. 240°
  C. 270°
  D. 360°

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  2. 16m2
  3. 10m2
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  2. 160m3
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  1. 50m2
  2. 100m2
  3. 150m2
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  4. 400m2
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  3. 15m
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1. What is the measure of ∠DAB?
  A. 60°
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  C. 120°
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