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Case Study – 2 Resident… (Class 10 Maths Basic 2024, Q37)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2024: question 37

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedCoordinate Geometry

Case Study – 2

Resident Welfare Association (RWA) of Gulmohar Society in Delhi, have installed three electric poles A, B and C in the society's common park. Despite these three poles, some parts of the park are still in the dark. So, RWA decides to have one more electric pole D in the park. The park can be modelled as a coordinate system given below.

On the basis of the above information, answer the following questions :

  1. (i)

    What is the position of the pole C ?

    1 mark
  2. (ii)

    What is the distance of the pole B from the corner O of the park ?

    1 mark
  3. (iii)(a)

    Find the position of the fourth pole D so that the four points A, B, C and D form a parallelogram ABCD.

    2 marks

  4. OR

    (iii)(b)

    Find the distance between poles A and C.

    2 marks

Figure in the paper: Coordinate graph with X-axis and Y-axis meeting at origin O, grid marked 1 to 6 on X and 1 to 10 on Y. Three poles drawn as dots with upward arrows: A at (2, 7) with its arrow going up to about 8; B at (6, 6) with arrow going up to about 7; C at (5, 4) with arrow going up to about 5. The park is the first-quadrant region shown. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/4/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Read the coordinates of each pole from the grid, x first and then y.

Hint 2

For distances, use ; for O, the coordinates are (0, 0).

Hint 3

In a parallelogram ABCD the diagonals AC and BD bisect each other, so their mid-points are the same.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. (i) Reading from the graph, pole C is at the point (5, 4).

    1 mark

  2. (ii) Pole B is at (6, 6) and O is at (0, 0).

    ½ mark

  3. By the distance formula, units.

    ½ mark

  4. (iii)(a) The poles are at A(2, 7), B(6, 6) and C(5, 4). Let D be .

    The diagonals of a parallelogram bisect each other, so the mid-point of AC equals the mid-point of BD:

    1 mark

  5. Comparing x-coordinates:

    ½ mark

  6. Comparing y-coordinates:

    So the fourth pole D is at (1, 5).

    ½ mark

  7. (iii)(b) The poles are at A(2, 7) and C(5, 4).

    1½ marks

  8. units

    ½ mark

Answer: (i) C(5, 4); (ii) units; (iii)(a) D(1, 5); (iii)(b) units

Where the marks are

  • (i) Writes C as (5, 4) (1 mark)
  • (ii) Takes B(6, 6) and applies the distance formula from O (½ mark)
  • (ii) BO = (½ mark)
  • (iii)(a) Equates the mid-points of the diagonals AC and BD (1 mark)
  • (iii)(a) Finds x = 1 (½ mark)
  • (iii)(a) Finds y = 5, so D(1, 5) (½ mark)
  • (iii)(b) Substitutes correctly in the distance formula for AC (1½ marks)
  • (iii)(b) AC = (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 430/4/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.