Points and Line

in 2-dimensional space

-Indra B. Kshattry PhD

Introduction:

A 2-dimensional (2D) plane is a flat surface that extends infinitely in two directions: length and width. It's characterized by two dimensions, often represented by the x-axis (horizontal) and y-axis (vertical) in a coordinate system.

Definition:

A 2-dimensional plane is a geometric surface that has:

In a Cartesian coordinate system, any point on the plane can be identified by a pair of coordinates (x, y). The intersection of the x-axis and y-axis is called the origin, denoted by (0, 0).

Properties:

Examples:

  1. Graph paper:

    Let's imagine a piece of graph paper. Each square on the paper represents a unit on the plane. One can plot points, draw shapes, and measure distances using the x and y coordinates.

  2. Computer screen:

    Our computer screen is a 2D plane. The screen pixels are arranged in a grid of rows (y-axis) and columns (x-axis). When we move your cursor, we navigate points on this 2D plane.

  3. Maps:

    Maps are another example of a 2D plane. Locations on a map are given by coordinates (latitude and longitude), which can be thought of as x and y coordinates.

  4. Art and designs:

    Drawing and painting on a canvas is done on a 2D plane. Artists use the x and y dimensions to create images, designs, and perspectives.

  5. Mathematics:

    In mathematics, a 2D plane is often used to solve geometry problems, graph equations, and study shapes like circles, triangles, and polygons.

  6. Visual representation:

    Let's refer the following simple graph, In this graph, the point (x, y) is a location on the 2D plane, defined by its distance from the x-axis and y-axis.

Scatter plot