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Orienting Yourself: The Use of Coordinates: CBSE Class 9 Mathematics practice questions

Practise 50 questions on Orienting Yourself: The Use of Coordinates, free, with an explanation for each answer.

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Sample questions

A city of the Sindhu-Sarasvatī Civilisation was built like a grid, with streets running North–South and East–West at regular gaps. Roughly how far apart were these streets?

Animation of a cart moving along the streets of a town laid out as a grid
  1. About 1 m
  2. About 10 m
  3. About 100 m
  4. About 1 km
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B. About 10 m

The streets were laid out with striking precision in North–South and East–West directions, about 10 metres apart. A merchant could find a shop by counting units of distance North–South and East–West from the city centre — a coordinate system in practice.

Using the feet (8,9)(8, 9), (11,9)(11, 9) and (11,7)(11, 7) of the study table (1 unit = 1 ft), what can you say about the table's size?

Part of the bedroom grid with three table feet marked
  1. 11 ft long and 9 ft wide; its height cannot be read from the plan
  2. 19 ft long and 16 ft wide; its height cannot be read from the plan
  3. 3 ft long and 2 ft wide; its height cannot be read from the plan
  4. 3 ft long, 2 ft wide and 9 ft high
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C. 3 ft long and 2 ft wide; its height cannot be read from the plan

Length =11−8=3= 11 - 8 = 3 ft and width =9−7=2= 9 - 7 = 2 ft. A floor plan is 2-D, so the height cannot be found from it. Reading a single coordinate (11 ft, 9 ft), adding coordinates (19 ft, 16 ft) or treating a y-coordinate as height are all mistakes.

The showering area SHWR in Reiaan's bathroom has corners S(−6,6)S(-6, 6), H(−3,6)H(-3, 6), W(−2,9)W(-2, 9) and R(−6,9)R(-6, 9) (1 unit = 1 ft). What is its floor area?

Animation of water drops in the shaded showering area SHWR on the bathroom grid
  1. 21 sq ft
  2. 12 sq ft
  3. 9 sq ft
  4. 10.5 sq ft
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D. 10.5 sq ft

SH and RW lie on y=6y = 6 and y=9y = 9, so they are parallel and SHWR is a trapezium. SH=−3−(−6)=3SH = -3 - (-6) = 3 ft, RW=−2−(−6)=4RW = -2 - (-6) = 4 ft and the height is 9−6=39 - 6 = 3 ft. Area=12(3+4)×3=10.5 sq ft\text{Area} = \tfrac{1}{2}(3 + 4) \times 3 = 10.5\ \text{sq ft} 21 forgets the 12\tfrac{1}{2}; 12 treats it as a 4×34 \times 3 rectangle; 9 as a 3×33 \times 3 square.

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