8th Grade - Translation


  • There are four different types of transformations.
    1. Dilations
    2. Reflections
    3. Rotations
    4. Translations
  • To transform a figure (shape) means changing the size, location, and direction it faces.
  • The figure before the transformation occurs is called the pre-image.
  • The figure after the transformation is called the image.
  • If the pre-image is labeled as A, then the image would then be labeled as A' (pronounced as "A prime").


  • Two images are congruent if they are of the same shape and size.
  • The image after translation is congruent to the pre-image.
  • Translations are rigid motions. Rigid motions preserve distance (side lengths) and angle measures.
  • The symbol for congruency is ≅.



  • A translation moves (slides) or displaces every point of the figure by the same distance and in the same direction
  • Translation in coordinate plane: x,y  x+a,y+a
  • In translation, the figure slides but never turns or rotates.
  • In translation, pre-image and image are congruent.
  • The figure can slide in any direction on the coordinate plane. 


Solved Examples

Question 1: A'B'C' is the translated image of ABC. What is the translation rule that models the given transformation?

Solution: From the graph, it is evident that each point of the pre-image is shifted 2 units to the left and 3 units upwards. Hence, the translation rule is x, yx-2, y+3


Question 2: The coordinates of a quadrilateral are shown in the table below. If the image has A' at a point -1,7, what are the coordinates of B',C' and D'?

Solution: To find the coordinates for these points, first identify the translation that moves the point A to A'. The x-coordinate moves from -3 to 1, so the horizontal movement is x+4. The y-coordinate moves from 6 to -7, so the vertical movement is y-13. Therefore, we want to translate each coordinate as x+4, y-13.

The coordinates of B' are x=1+4=5, and y=4-13=-9. Point B' is at 5, -9.

The coordinates of C' are x=-7+4=-3, and y=-5-13=-18. Point B' is at -3, -18.

The coordinates of D' are x=-6+4=-2, and y=-2-13=-15. Point B' is at -2, -15.

Cheat Sheet

  • The algebraic representation of a translation depends on the directions of the displacement.
  • When the x-values are changed, the figure moves horizontally (left or right).
  • When the y-values are changed, the figure moves vertically (up or down).


Blunder Areas

  • Differentiate between pre-image (A) and image (A').
  • Think of the movements in terms of positive and negative. 
  • Movements to the right and up are positive.
  • Movements to the left and down are negative.
  • Horizontal (left and right) movements change the x-values.
  • Vertical (up and down) movements change the y-values.