Chapter 7: Coordinate Geometry
Using algebra to study geometry: Distance, Section formulas, and Mid-points.
📏 The Distance Formula
Finds the distance between any two points P(x1, y1) and Q(x2, y2). Derived using Pythagoras Theorem.
🔗 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.
⭐ 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. 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.
Parallelogram Diagonal Trick
Diagonals of a parallelogram bisect each other. 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). A point on the y-axis is ALWAYS (0, y). 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.
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!