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MathidiaMathematics Academy
Transformations and vectors
Lesson 58 of 75
Standard practice

Vector notation

Objective. Represent movement using column vectors.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Vector notation represents movement using a column vector, written as (x, y) stacked vertically, where the top number shows horizontal movement (positive is right, negative is left) and the bottom number shows vertical movement (positive is up, negative is down). A vector such as (3 over −2) means moving 3 units right and 2 units down from a starting point. Unlike coordinates, which describe a fixed position, a vector describes a movement or displacement that can be applied starting from anywhere. Vectors are often labelled with a single bold letter or an arrow over two points, such as the vector from A to B written as AB with an arrow.

Worked example

A point starts at (2, 5) and is translated by the vector (4 over −3). Find the coordinates of the new point.

2 … 5
Coordinate grid with the line 2 … 5
  1. 1The vector means move 4 units right and 3 units down.
  2. 2Apply the horizontal movement: 2 + 4 = 6.
  3. 3Apply the vertical movement: 5 − 3 = 2.
  4. 4The new point is (6, 2).

Answer: (6, 2)

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Practice

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Common mistake. Pupils sometimes confuse a vector's column notation with coordinates, treating (3 over −2) as a fixed point rather than a movement of 3 right and 2 down from wherever it starts. Remember a column vector describes a displacement, not a location.

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