Introduction to Rectangular Cartesian Coordinates for JEE Main

The chapter Rectangular Cartesian Coordinates is a fundamental topic in Class 11 Maths, forming the basis for coordinate geometry, straight lines, and 3D geometry.

In Cartesian coordinates, points in a plane are represented using two perpendicular axes – X-axis and Y-axis. Understanding distance formula, midpoint formula, slope, and collinearity is essential for solving numerical and conceptual problems efficiently.

Direct Links to Download JEE Main - Chapter Wise Previous Year Papers Maths (PDF)

► Click “Download Here” next to your subject to access the free PDF.

Coordinate System

1. Definition:

• A rectangular Cartesian coordinate system consists of two perpendicular axes (X-axis and Y-axis) intersecting at the origin O(0, 0).

2. Coordinates of a Point:

• A point P in the plane is represented as P(x, y)

• x = distance from Y-axis, y = distance from X-axis

3. Quadrants:

• First quadrant: x > 0, y > 0

• Second quadrant: x < 0, y > 0

• Third quadrant: x < 0, y < 0

• Fourth quadrant: x > 0, y < 0

Distance Formula Between Two Points

• Distance between points P₁(x₁, y₁) and P₂(x₂, y₂):
  d = √[(x₂ – x₁)² + (y₂ – y₁)²]

Example: Distance between A(2, 3) and B(5, 7) → √[(5–2)² + (7–3)²] = √(9 +16) = √25 = 5

Midpoint Formula

• Midpoint M of line segment joining P₁(x₁, y₁) and P₂(x₂, y₂):
  M = ((x₁ + x₂)/2 , (y₁ + y₂)/2)

Example: Midpoint of A(2, 3) and B(4, 7) → ((2+4)/2 , (3+7)/2) = (3, 5)

Slope of a Line

• Slope (m) of line joining points P₁(x₁, y₁) and P₂(x₂, y₂):
  m = (y₂ – y₁) / (x₂ – x₁)

• Special cases:

  • Horizontal line → slope = 0

  • Vertical line → slope = undefined

Example: Slope of line joining (1, 2) and (4, 8) → m = (8–2)/(4–1) = 6/3 = 2

Collinearity of Points

• Three points P₁(x₁, y₁), P₂(x₂, y₂), P₃(x₃, y₃) are collinear if slope of P₁P₂ = slope of P₂P₃

• Condition: (y₂ – y₁)/(x₂ – x₁) = (y₃ – y₂)/(x₃ – x₂)

Example: Check if points (1, 2), (3, 6), (5, 10) are collinear:

• Slope of first pair = (6–2)/(3–1) = 4/2 = 2

• Slope of second pair = (10–6)/(5–3) = 4/2 = 2 → Collinear

Section Formula

• Coordinates of a point dividing line joining P₁(x₁, y₁) and P₂(x₂, y₂) in ratio m:n:
  (mx₂ + nx₁)/(m+n) , (my₂ + ny₁)/(m+n)

Example: Point dividing (2, 3) and (4, 7) in ratio 1:1 → ((4+2)/2 , (7+3)/2) = (3, 5)

Applications of Rectangular Cartesian Coordinates in JEE Main

• Solve distance, midpoint, and collinearity problems

• Analyze geometry of points and lines in the plane

• Basis for straight line, circle, parabola, and 3D geometry problems

• Frequently tested in MCQs, integer-type, and numerical problems

Example: Find the distance between two points, midpoint, and slope in a plane problem in JEE Main.

Important JEE Main Preparation Tips for Rectangular Cartesian Coordinates

• Memorize distance, midpoint, and slope formulas

• Practice collinearity and section formula problems

• Solve geometrical problems using coordinates

• Use diagrams for visualization

• Solve previous year JEE Main MCQs and numerical problems

Why Study Rectangular Cartesian Coordinates from Studentbro.in?

Studentbro.in provides:

• Step-by-step explanations of distance formula, midpoint, slope, and collinearity

• Solved examples for line segment, points, and geometrical problems

• Diagrams and charts for quick understanding

• MCQs and PYQs aligned with JEE Main syllabus

Conclusion

The Rectangular Cartesian Coordinates chapter is a fundamental and scoring topic in Class 11 Maths for JEE Main. Mastery of coordinates of points, distance, midpoint, slope, collinearity, and section formula helps students solve conceptual and numerical problems efficiently.

Studentbro.in provides structured, easy-to-understand, and exam-focused content to master Rectangular Cartesian Coordinates effectively and boost JEE Main scores.