CBSE Class 10 Maths: Coordinate Geometry — Complete Notes 2026

Distance Formula

• Distance between P(x₁,y₁) and Q(x₂,y₂): PQ = √[(x₂−x₁)² + (y₂−y₁)²]
• Derived from Pythagoras' theorem on right triangle with horizontal and vertical legs
• Application: check if points form equilateral triangle (all sides equal), right triangle (Pythagoras), collinear (sum of two distances = third)

Section Formula

• Point P dividing AB in ratio m:n internally: P = [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)]
• Midpoint formula (m = n = 1): M = [(x₁+x₂)/2, (y₁+y₂)/2]
• External division: P = [(mx₂−nx₁)/(m−n), (my₂−ny₁)/(m−n)]; CBSE may ask both types

Area of a Triangle

• Area = ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|; use absolute value (area always positive)
• Collinearity test: if area = 0, three points are collinear
• CBSE application: find value of k if three points are collinear; or find area of quadrilateral by dividing into two triangles

Centroid of a Triangle

• Centroid G = [(x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3]; intersection of medians
• Not in CBSE Class 10 syllabus but useful knowledge for Class 11/JEE preparation
• CBSE may use midpoint formula to find centroid indirectly

Straight Lines Basics

• Slope of line through (x₁,y₁) and (x₂,y₂): m = (y₂−y₁)/(x₂−x₁)
• Equation of line: y − y₁ = m(x − x₁); or y = mx + c (slope-intercept form)
• CBSE may not ask full line equations in Class 10 but slope and parallel/perpendicular conditions appear

Typical CBSE Question Types

• Find ratio in which a point divides a line segment: use section formula, equate x or y coordinate
• Prove that points form a rectangle/rhombus: verify using distance formula and diagonals
• Find unknown coordinate if area of triangle is given: set up area equation, solve

Common Mistakes

• Not taking absolute value in area formula → negative answer
• Swapping x and y coordinates in distance formula
• In section formula: ratio m:n means P divides from first point to second; confusion about which point is which