Translations

1
Translations

• A translation shifts every point of a figure the
  same distance in the same direction.
• A figure that is transformed by a translation
  remains congruent to its preimage.
• Its side lengths, angle measures, and other
  properties remain the same.
• Translation changes nothing but the location of a
  figure

2
ISOMETRY

• An isometry is any transformation that does not
  change the size and shape of the transformed
  figure.

3
Translation

• A translation is an isometry, meaning the
  preimage and its translated image are the same
  size and shape.
• When a point A is transformed, the image is
  labeled A' (read A prime).

4
Translations in 1 dimension

• A square has vertices A(1,1), B(4,1), C(4,4), and
  D(1,4)
• Graph
• Find the coordinates of the vertices of the image
  of square ABCD after a translation of 5 units to
  the right.
• Show the preimage and image on the same graph.
• Find the areas of both squares.

5
Mapping notation

• Mapping notation is used to indicate the way in
  which a point or several points should be
  transformed.
• ex. T (x,y) (x1, y -2)
• This says that the original pair of coordinates
  will be changed into
• (x1,y-2) or the x coordinate will increase by 1
  and the y coordinate will decrease by 2

6
Translations in 2 dimensions

• The vertices of a quadrilateral are
• D(-5,2), E(-3,-2), F(0,0), and G(-2,0)
• Find the image of D'E'F'G' after the translation
• T(x,y) (x6,y-3)

7
Showing translations with vectors.

• A translation for a polygon can also be
  represented using a vector.
• Quad ABCD has points A(0,0), B(0,4), C(4,4) and
  D(4,0)
• Find the image of ABCD under the translation
  vector (2,3)
• 1. draw ABCD
• 2. place the initial point of the vector on A and
  draw the vector, which moves the point 2 units
  right and 3 units up. Where is point A'?
• Repeat this process for B,C,D to find B', C', and
  D'

8
practice

• A line segment has endpoints A(11,5) and B(4,9).
  It is translated 5 units up. What are the
  coordinates of A' and B'?
• A triangle has vertices K(2,5), L(1,11) and
  M(5,7). Find the image of Tri KLM after the
  translation
• T (x,y) (x-2,y1)

9
practice

• Find the coordinates of the vertices of the image
  of parallelogram ABCD with coordinates A(2,4),
  B(7,4), C(10,6) and D(5,6) after the translation
  by the vector (3,1)