Coordinate Geometry CBQs — CBSE Class 10 (2027) with step-wise solutions

Sample Coordinate Geometry CBQs

1. Question 1MCQ1 mark
   On a scorer's chart of a cricket ground, the stumps at the bowler's end are at O(0, 0) and every unit is 1 m. A fielder picks up the ball at F(-18, 24) and throws it straight at these stumps. How far does the ball travel to reach the stumps?
   • 30 m
   • 42 m
   • 6 m
   • √252 m
   Show step-wise solution

   1. [1 mark] OF = √[(-18 - 0)² + (24 - 0)²] = √(324 + 576) = √900 = 30 m.

   Answer: 30 m

2. Question 2MCQ1 mark
   On a city map (1 unit = 1 km) the railway station is at R(-4, 7) and the bus depot is at B(10, -3). The city plans a metro station exactly halfway between them on the straight road joining R and B. At which point should the metro station be built?
   • (7, -5)
   • (3, 2)
   • (6, 4)
   • (14, -10)
   Show step-wise solution

   1. [1 mark] Midpoint of RB = ((-4 + 10)/2, (7 + (-3))/2) = (6/2, 4/2) = (3, 2).

   Answer: (3, 2)

3. Question 3Assertion-Reason1 mark
   On a district map (1 unit = 1 km) a post office is at P(-2, 3) and a police station is at Q(4, -5). Assertion (A): The straight-line distance between the post office and the police station is 8 km. Reason (R): The distance between the points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].
   • (A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
   • (B) Both Assertion and Reason are true but Reason is NOT the correct explanation of Assertion.
   • (C) Assertion is true but Reason is false.
   • (D) Assertion is false but Reason is true.
   Show step-wise solution

   1. [1 mark] (D): PQ = √[(4 + 2)² + (-5 - 3)²] = √(36 + 64) = √100 = 10 km, not 8 km, so A is false; R is the correct distance formula, so R is true.

   Answer: (D)

4. Question 4Short answer2 marks
   A drone delivery company plots its locations on a city grid in which 1 unit = 1 km. Its warehouse is at W(2, 3) and a customer's house is at H(10, 9). The drone flies along the straight line from W to H. Find the distance the drone flies.
   Show step-wise solution

   1. [1 mark] WH = √[(10 − 2)² + (9 − 3)²] = √(8² + 6²) = √(64 + 36).
   2. [1 mark] WH = √100 = 10 units, so the drone flies 10 km.

   Answer: 10 km

5. Question 5Case study4 marks
   For the annual day, the stage of a school auditorium is marked as a coordinate grid with 1 unit = 1 m. A straight lighting bar runs from bracket L1(−4, 6) to bracket L2(8, 0). The lead singer stands at S(3, 0). Based on the above information, answer the following questions: (i) Find the coordinates of the mid-point M of the lighting bar. (ii) A spotlight P is clamped on the bar so that it divides L1L2 in the ratio 1 : 2. Find the coordinates of P. (iii) Find the distance of the singer from P and from M, and state which of the two is nearer to her.
   Show step-wise solution

   1. [1 mark] (i) M = ((−4 + 8)/2, (6 + 0)/2) = (2, 3).
   2. [1 mark] (ii) P = ((1 × 8 + 2 × (−4))/3, (1 × 0 + 2 × 6)/3) = (0/3, 12/3) = (0, 4).
   3. [1 mark] (iii) SP = √((3 − 0)² + (0 − 4)²) = √(9 + 16) = 5 m; SM = √((3 − 2)² + (0 − 3)²) = √(1 + 9) = √10 m.
   4. [1 mark] (iii) Since 10 < 25, √10 < 5, so M is nearer to the singer, at √10 m (SP = 5 m).

   Answer: (i) M(2, 3) (ii) P(0, 4) (iii) SP = 5 m, SM = √10 m; M is nearer

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