Concept of Position, Distance, and Displacement in Relation to X-Y Plane – SS2 Physics Lesson Note (First Term)

Position is the point at which an object can be located relative to a given point called the origin. Distance is the separation between two points and is a scalar quantity, while displacement is the distance covered in a specified direction and is a vector quantity. Positions are located using a coordinate system.

Behavioural objectives

By the end of the lesson, students should be able to:

• define position and explain the role of the origin;
• describe the rectangular Cartesian coordinate system;
• distinguish between a plane and a space;
• define distance and state that it is a scalar quantity;
• define displacement and state that it is a vector quantity.

What is position?

The position of an object in space or on a plane is the point at which the object can be located relative to a given point (the origin).

What is a coordinate system?

Rectangular Cartesian coordinate system

This is a system that consists of two or three intersecting lines that are mutually perpendicular. It serves as a reference frame that guides one in locating the position of a point in a plane or in space.

The system also assigns direction (with an arrowhead) to these reference lines, which are called the coordinate axes. Distances measured from the point of intersection (known as the origin) are positive along OX, OY and OZ. Distances measured in the opposite direction are negative.

Plane

A plane is a geometric figure defined by a 2-dimensional coordinate system, which has two reference axes.

Space

A space is defined by a 3-dimensional coordinate system, which has three reference axes.

What is distance?

Distance is a measure of the separation between two points. It has magnitude but no direction, so it is a scalar quantity.

Determining the distance between two points

Two points A and B in a plane are defined by two ordered pairs of values, (x₁, y₁) and (x₂, y₂). In space, they are defined by (x₁, y₁, z₁) and (x₂, y₂, z₂). The distance between them can be found using these relations:

• In a plane: d = √[(x₂ – x₁)² + (y₂ – y₁)²]
• In space: d = √[(x₂ – x₁)² + (y₂ – y₁)² + (z₂ – z₁)²]

What is displacement?

Displacement is the distance covered in a specified direction. It is a vector quantity, which has the same unit as distance.

Evaluation

1. Define the position of an object.
2. What is the origin in a rectangular Cartesian coordinate system?
3. Why is distance a scalar quantity?
4. Define displacement and state its unit relative to that of distance.

Assignment

Highlight three differences between distance and displacement.