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MathidiaMathematics Academy
Coordinates, graphs and transformations
Lesson 70 of 75
Review

Translations

Objective. Describe and perform translations using horizontal and vertical movement.

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

Learn: the key idea

A translation is a transformation that slides every point of a shape the same distance in the same direction, without rotating, reflecting or resizing it. A translation is described using a column vector such as (3,−2), which moves every point 3 units right and 2 units down. To translate a coordinate, add the vector's horizontal component to the x-coordinate and the vertical component to the y-coordinate. For example, translating the point (1,4) by the vector (2,−3) gives (1+2,4−3)=(3,1).

Worked example

A point (−2, 5) is translated by the vector (4, −6). Find the coordinates of the image after the translation.

2 … 5
Coordinate grid with the line 2 … 5
  1. 1Identify the horizontal component of the vector: 4.
  2. 2Add it to the x-coordinate: −2+4=2.
  3. 3Identify the vertical component of the vector: −6.
  4. 4Add it to the y-coordinate: 5+(−6)=−1.

Answer: (2, −1)

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Common mistake. Pupils sometimes subtract the vector components instead of adding them, or apply them to the wrong coordinate. Always add the top number of the vector to x and the bottom number to y.

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