ICSE Class 10 Maths: Coordinate Geometry — Complete Notes 2026

Coordinate System Revision

• Cartesian plane: x-axis (horizontal), y-axis (vertical); four quadrants
• Distance formula: d = √[(x₂−x₁)² + (y₂−y₁)²]
• Application: verify if points form a specific shape (equilateral triangle, square)

Section Formula

• Point P dividing A(x₁,y₁) and B(x₂,y₂) in ratio m:n internally: ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
• Midpoint formula: special case m:n = 1:1; M = ((x₁+x₂)/2, (y₁+y₂)/2)
• External division: change sign of n in internal formula

Area of Triangle Using Coordinates

• Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|
• If area = 0, points are collinear (use to test collinearity)
• Area of quadrilateral: split into two triangles or use shoelace formula

Equation of a Straight Line

• Slope-intercept form: y = mx + c; m = tan θ = slope; c = y-intercept
• Point-slope form: y − y₁ = m(x − x₁)
• Two-point form: (y − y₁)/(x − x₁) = (y₂ − y₁)/(x₂ − x₁)

Slope and Perpendicularity

• Slope of line through two points: m = (y₂−y₁)/(x₂−x₁)
• Parallel lines: equal slopes (m₁ = m₂); perpendicular lines: m₁ × m₂ = −1
• Horizontal line: slope = 0; vertical line: slope undefined

Intercept Form and Standard Form

• Intercept form: x/a + y/b = 1 (a and b are x and y intercepts)
• General form: ax + by + c = 0; convert to slope-intercept to find m and c
• Find equation of perpendicular bisector of line segment

ICSE Numericals — Coordinate Geometry

• Find k if (1, k), (2, 4) and (5, 10) are collinear
• P divides A(2,3) and B(8,9) in ratio 2:1; find P
• Find equation of line perpendicular to 3x + 4y = 12 and passing through (1, 2)