A fast, one-glance recap of Class 10 Maths Chapter 7 (Coordinate Geometry) — for full worked explanations, see the Solutions.
Revision Notes: Coordinate Geometry
- Distance formula: d=√((x₂-x₁)²+(y₂-y₁)²)
- Distance from origin: √(x²+y²)
- Section formula (ratio m:n, internal): ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n))
- Midpoint formula (m=n): ((x₁+x₂)/2, (y₁+y₂)/2)
- Collinearity test: three points are collinear if the area of the triangle they form is 0
- Area of a triangle: ½|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|
- Locus equidistant from two points: the perpendicular bisector of the segment joining them
- Type of quadrilateral: use all 4 sides + both diagonals together (equal sides + equal diagonals = square; equal sides only = rhombus; opposite sides equal = parallelogram)
- 2023 rationalisation: only Ex 7.1 (Distance Formula) and Ex 7.2 (Section Formula) remain as numbered exercises — the old Ex 7.3 (Area of a Triangle) and Ex 7.4 (Optional) were removed, though the area formula itself remains useful (see Extra Questions)
See also: Extra Questions (HOTS) | Formulas Handbook
