Class 9 · Chapter 1

Orienting Yourself: The Use of Coordinates

Cartesian plane, plotting points, distance and midpoint.

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Ganita Manjari · Class 9 (2026-27)

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Tip: NCERT updated the syllabus for 2026-27. The links above open the latest edition on the official portal — chapter titles and numbering may differ from the notes shown here.

Detailed theory

Descartes' breakthrough: turn geometry into algebra. Each point in the plane corresponds uniquely to an ordered pair

(x, y)

Key concepts & formulas

Cartesian plane: two perpendicular axes at origin

(0,0)

Point

P(x, y)

x

horizontal,

y

vertical.

Quadrants I

(+,+)

, II

(-,+)

, III

(-,-)

, IV

(+,-)

Distance formula:

d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

Midpoint:

M = \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)