CBSE Class 10 Maths Chapter 7 Notes Coordinate Geometry

Coordinate Geometry Class 10 Notes Understanding the Lesson

Distance formula

1. The distance between two points A(x₁, y₁) and B(x₂, y₂) is

2. The distance of point A(x, y) from origin 0(0, 0) is
\(\mathrm{AO}=\sqrt{x^{2}+y^{2}}\)

3. Three given points will form:

• Right angled triangle if sum of squares of any two sides is equal to the square of third (largest) side.
• Equilateral triangle if length of all three sides are equal.
• Isosceles triangle if length of any two sides are equal.
• A line or collinear if sum of two sides is equal to third side.

4. Four given points will form:

• Square if length of all four sides are equal and diagonals are equal.
• Rhombus if length of all four sides are equal.
• Rectangle if opposite sides are equal and diagonals are equal.
• Parallelogram if opposite sides are equal.

Section formula
I. If A(x₁, y₁) and BB(x₂, y₂)) are two points on a plane and P(x, y) divides AB internally in the ratio m : n, then co-ordinates of P are given by

Area of a Triangle

1. Area of ΔABC formed by vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) is given by
Ar(ΔABC) =\(\frac{1}{2}\) (- y₃) + x₂ (y₃ – y₁)+ x₃(y₁ – y₂)]
[Only positive numerical value to be taken]

2. If Ar(ΔABC) = 0, then A, B and C are collinear points.

3. If‘C’ is centroid of a triangle, the median is divided in the ratio 2 : 1 by C and coordinates of C are
\(\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)\)

4. Area of quadrilateral LMNO = ar(ΔLMO) + ar(ΔNMO)