Chapter 7

Introduction to Coordinate Geometry

Coordinate plane: The coordinate plane is a basic concept for coordinate geometry. It describes a two-dimensional plane in terms of two perpendicular axes: x and y.

The distance of a point from the y-axis is called its x-coordinate, or abscissa.

The distance of a point from the x-axis is called its y-coordinate, or ordinate.

These distances form the coordinates of a point (x, y).

The coordinates of a point on the x-axis are (x, 0).

The coordinates of a point on the y-axis are (0, y).

Distance formula: The distance between the points A (x₁, y₁) and B (x₂, y₂) is given by

Note: The distance of a point A (x, y) from the origin O (0, 0) is given by

Section formula: The co-ordinates of the point R (x, y) which divides the line segment joining the points P (x₁, y₁) and Q (x₂, y₂), internally, in the ratio m₁ : m₂ are given by

Note: If R does not lie between P and Q but lies on the line PQ, outside the line segment PQ, and RP: RQ = m₁ : m₂, we say that R divides externally the line segment joining the points P and Q and the co-ordinates of the point R (x, y) are given by .

Mid-point formula: The mid-point R (x, y) of a line segment joining the points P (x₁, y₁) and Q (x₂, y₂) is given by

In this case the point R (x, y) divides the line segment joining points P (x₁, y₁) and Q (x₂, y₂) in the ratio 1 : 1.

Area of triangle:

Generally, area of a triangle = ½ × Base × Altitude

If the coordinates of vertices of a triangle PQR are P (x₁, y₁), Q (x₂, y₂) and R (x₃, y₃), then the area of the triangle is given by

Area of triangle PQR =