Coordinate Geometry — Notes
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01
7.1 Distance Formula
For A(x1,y1) and B(x2,y2):
AB = √[(x2−x1)2+(y2−y1)2].
AB = √[(x2−x1)2+(y2−y1)2].
02
7.2 Section Formula
If P divides the line segment joining A(x1,y1) and B(x2,y2) internally in the ratio m:n, then:
P = ((mx2+nx1)/(m+n), (my2+ny1)/(m+n)).
P = ((mx2+nx1)/(m+n), (my2+ny1)/(m+n)).
03
7.3 Midpoint Formula
The midpoint of A(x1,y1) and B(x2,y2) is ((x1+x2)/2,(y1+y2)/2).
04
7.4 Area of a Triangle
For vertices (x1,y1), (x2,y2), (x3,y3):
Area = 1/2 |x1(y2−y3) + x2(y3−y1) + x3(y1−y2)|.
Area = 1/2 |x1(y2−y3) + x2(y3−y1) + x3(y1−y2)|.
Collinearity
If the area of the triangle formed by three points is zero, the three points are collinear.
⚡ Quick Revision
- Distance formula comes from Pythagoras.
- Section formula uses the internal division ratio.
- Midpoint is the section formula with m=n.
- Area = 0 means collinear points.
🎯 Board Exam Focus
- Use absolute value in the area formula.
- Check which point receives m and n in the section formula.
- Simplify squared differences carefully.
🚀 Last-Minute Revision
✔ Read every formula with its conditions and symbols.
✔ Write given data first and keep units consistent.
✔ For proofs, state the theorem and show logical steps.
✔ Check signs, substitutions and final units.
❤️ Examisthan.com • Class 10 CBSE Mathematics • Chapter 7: Coordinate Geometry