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MathidiaMathematics Academy
Transformations
Lesson 53 of 75
Standard practice

Translation vectors

Objective. Describe translations using vectors.

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

Learn: the key idea

A translation slides every point of a shape the same distance in the same direction without turning or resizing it. This movement is described by a column vector, written as the horizontal shift on top and the vertical shift below, such as (3 above, −2 below) meaning 3 right and 2 down. To find the image of a point under a translation, add the vector's components to the point's coordinates separately. Example: translating (1, 4) by the vector with 3 on top and −2 below gives (1 + 3, 4 − 2) = (4, 2).

Worked example

A point (−3, 2) is translated by the vector with 5 on top and −4 below. Find the image of the translation.

3 … 2
Illustrated card showing 3 … 2
  1. 1Add the top vector value to the x-coordinate: −3 + 5 = 2.
  2. 2Add the bottom vector value to the y-coordinate: 2 + (−4) = −2.
  3. 3Combine these results as a new coordinate pair.
  4. 4The image point is (2, −2).

Answer: (2, −2)

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Common mistake. Pupils sometimes add the vector components the wrong way round, treating the top number as vertical movement; always read the top of the vector as horizontal (x) and the bottom as vertical (y).

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