ICSE Class 10 Mathematics: Coordinate Geometry — Important Questions with Answers 2026

Short Answer Questions (2-3 Marks)

• Q: Find the distance between points A(3, 4) and B(-1, 2).
  Ans: Distance = √[(x₂-x₁)² + (y₂-y₁)²] = √[(-1-3)² + (2-4)²] = √[16 + 4] = √20 = 2√5 units.
• Q: Find the midpoint of the line segment joining (5, -3) and (-1, 7).
  Ans: Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) = ((5-1)/2, (-3+7)/2) = (4/2, 4/2) = (2, 2).
• Q: Find the equation of line passing through (2, 3) with slope 4.
  Ans: Using point-slope form: y - y₁ = m(x - x₁). y - 3 = 4(x - 2). y - 3 = 4x - 8. y = 4x - 5 or 4x - y - 5 = 0.

Long Answer / Application Questions (4-6 Marks)

• Q: Find the slope of line passing through (1, 5) and (4, -1).
  Ans: Slope m = (y₂ - y₁)/(x₂ - x₁) = (-1 - 5)/(4 - 1) = -6/3 = -2.
• Q: Find the section ratio in which point (3, 5) divides the join of (1, 2) and (7, 11).
  Ans: Using section formula: 3 = (7m + 1n)/(m+n) and 5 = (11m + 2n)/(m+n). From first: 3m + 3n = 7m + n → 2n = 4m → m/n = 1/2. Ratio = 1:2 (internal division). Verify: 5 = (11(1) + 2(2))/(1+2) = 15/3 = 5 ✓

Exam Tips for This Chapter

• Revise all definitions and laws from Coordinate Geometry — they are commonly asked as 1-2 mark questions
• Practice diagrams related to Coordinate Geometry — neat labelled diagrams carry 2-3 marks
• For numericals, always show formula → substitution → answer with correct units
• Previous year analysis shows Coordinate Geometry carries 8-12 marks in the board exam