CBSE · Class 6-12

Class 9 · Ganita Manjari

Unit 1 · Class 9Ganita Manjari

Orienting Yourself: The Use of Coordinates

Cartesian plane, plotting points, distance and midpoint.

Lessons

4 concepts

1
The Cartesian Plane
Descartes' breakthrough: turn geometry into algebra. Each point in the plane corresponds uniquely to an ordered pair $(x, y)$ .
2
Plotting Points
Start at origin. Move $x$ right (or left if negative), then $y$ up (or down). Mark the point and label it.
3
Distance Formula
Derived from Pythagoras: horizontal leg $(x_2-x_1)$ , vertical leg $(y_2-y_1)$ , hypotenuse is the distance.
4
Midpoint & Section Formulas
Midpoint is the average. Section formula generalises: point dividing $AB$ in ratio $m:n$ is $\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)$ .

Skills to practise

Skill · medium

Orienting Yourself: The Use of Coordinates — Practice