Class 10 · Chapter 7

Coordinate Geometry

Distance formula, section formula, area of a triangle from coordinates.

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Tip: open the NCERT PDF for the original chapter text alongside the notes here.

Detailed theory

The plane is divided into 4 quadrants by the

x

- and

y

-axes at the origin. A point

P(x, y)

has abscissa

x

(distance from

y

-axis) and ordinate

y

(from

x

-axis). Signs of coordinates identify the quadrant.

Key concepts & formulas

Distance

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

Section formula (internal, ratio

m:n

\left(\dfrac{mx_2+nx_1}{m+n},\; \dfrac{my_2+ny_1}{m+n}\right)

Midpoint:

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

Area of triangle

=\tfrac{1}{2}\big|x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)\big|

Collinear: area of triangle

= 0

Distance from origin:

\sqrt{x^2 + y^2}