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Carpooling is the… (Class 10 Maths Basic SQP 2025-26, Q36)

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MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 36

From the official CBSE sample question paper for 2025-26, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedCoordinate Geometry

Carpooling is the sharing of car journeys so that more than one person travels in a car, and prevents the need for others to have to drive to a location themselves. By having more people using one vehicle, carpooling reduces each person's travel costs such as: fuel costs, tolls, and the stress of driving. Carpooling is also a more environmentally friendly and sustainable way to travel as sharing journeys reduces air pollution, carbon emissions, traffic congestion on the roads, and the need for parking spaces.

Three friends Amar, Bhavin and Chetanya live in societies represented by the points A(4,5), B(6,2) and C(2,6) respectively. They all work in offices located in a same building represented by the point O(0,0). Since they all go to same building every day, they decided to do carpooling to save money on petrol. Based on the above information, answer the following questions.

  1. (i)

    What is the distance between B and C?

    1 mark
  2. (ii)

    If Bhavin and Chetanya planned to meet at a club situated at the mid-point of the line joining the points B and C, find the coordinates of this point.

    1 mark
  3. (iii)

    (A) Which society is farthest from the office? Also find its distance from the office.

    2 marks

  4. OR

    (iii)

    (B) Out of B and C which society is nearer to A? Also find their distances.

    2 marks

Figure in the paper: Coordinate graph with axes marked 5, 10, 15 on both axes, origin O. Points plotted: C(2,6) in blue, A(4,5) in red, B(6,2) in green, and O(0,0). See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Use the distance formula and the mid-point formula .

Hint 2

For distances from the office, one point is the origin, so the distance is just .

Hint 3

To compare distances, compare the numbers under the square roots.

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) units

    1 mark

  2. (ii) Mid-point of

    1 mark

  3. (iii)(A) Using the distance formula from :

    • units
    • units
    • units
    1½ marks

  4. (iii)(A) Since , society A is the farthest from the office, at a distance of units.

    ½ mark

  5. (iii)(B) units

    units

    1½ marks

  6. (iii)(B) Since , society C is nearer to A.

    ½ mark

Answer: (i) units; (ii) (4, 4); (iii)(A) Society A, units; (iii)(B) C is nearer, with AB = units and AC = units

Where the marks are

  • (i) BC = units (1 mark)
  • (ii) Mid-point (4, 4) (1 mark)
  • (iii)(A) OA = , OB = OC = units (1½ marks); concludes A is farthest (½ mark)
  • (iii)(B) AB = , AC = units (1½ marks); concludes C is nearer (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 paperSample paper 2025-26 (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.