Class 10 Maths Chapter 7: Coordinate Geometry Concept Infographic

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Chapter 7: Coordinate Geometry

Using algebra to study geometry: Distance, Section formulas, and Mid-points[cite: 8].

📏 The Distance Formula

Finds the distance between any two points P(x₁, y₁) and Q(x₂, y₂). Derived using Pythagoras Theorem[cite: 8].

PQ = √ (x₂ - x₁)² + (y₂ - y₁)² 

Distance from Origin (0,0):

OP = √ x² + y² [cite: 8]

🔗 The Section Formula

Finds coordinates of a point P(x, y) that divides the line joining A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁ : m₂[cite: 8].

x =

m₁x₂ + m₂x₁m₁ + m₂

,   y =

m₁y₂ + m₂y₁m₁ + m₂

Mid-Point Formula (Ratio 1:1):

P(x, y) = [

x₁ + x₂2

,

y₁ + y₂2

][cite: 8]

⭐ Board Exam Super-Hacks

The "k : 1" Ratio Trick

If you need to find the RATIO in which a point divides a line, always assume the ratio is k : 1 instead of m₁ : m₂[cite: 8]. It makes the calculation 10x faster!

Points of Trisection

Trisection means dividing into 3 equal parts. The two points dividing the line will use ratios 1 : 2 and 2 : 1[cite: 8].

Parallelogram Diagonal Trick

Diagonals of a parallelogram bisect each other[cite: 8]. Equate the mid-point of diagonal AC to the mid-point of diagonal BD to find missing vertices!

⚠️ Common Exam Traps

Trap 1: Axis Confusion

A point lying on the x-axis is ALWAYS of the form (x, 0)[cite: 8]. A point on the y-axis is ALWAYS (0, y)[cite: 8]. Don't mix these up when setting up equidistant equations!

Trap 2: Proving a Square

To prove 4 points form a square, showing all 4 sides are equal is NOT ENOUGH (that could just be a rhombus). You MUST also show that the two diagonals are equal[cite: 8].

Trap 3: Sign Mistakes in Distance

When subtracting coordinates like (x₂ - x₁) where x₁ is negative, remember two negatives make a positive! e.g., (2 - (-3))² = (2 + 3)² = 25. Always use brackets!

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