Introduction to Transformations

A translation moves a given object a certain distance based on a specific command.

For example, take ∆ ABC. Under the transformation: 4 inches right and 2 inches down.

A

B C

The new position would be…

(Note the ´ after the A, B, and C of the second triangle) A’

This denotes prime notation.

B´ C´

Now you try:

Given the commands, translate each object to its desired location.

1. Plot point A (2, 3). The move it 4 places left and 3 places down. What is the new coordinates for the point A?

2. Plot point B (-7, 3). Then move the point 6 places in the positive x direction, and 5 places in the negative y direction.

3. Plot the triangle ABC at the points A (0, 5) B (3, 2) and C (-2, -2). Then translate the triangle (each point) down 2 and right 3.

4. Draw pentagon DEFGH with vertices at D (1, 1) E (3, 3) F (0, 5) G (4, -2) and H (2, -4). Translate this pentagon so that all 5 points are in quadrants 2 and 3.

A translation can be notated using pointed brackets and a pair of numbers, like <4,3>. The pointed brackets are used to indicate a vector and the numbers inside are an “x” value and a “y” value. This denotes the movement of a point in the “x” direction and in the “y” direction.

Example 1: Translate point A using the vector <-3, -5>

<negative 3 in the x, negative 5 in the y>

Before the translation: Under the translation:

Point A (4, 4)

A. Rewrite the commands given on the previous 4 practice problems in correct notation using the pointed brackets.

1.) < , > 2.) < , > 3.) < , > 4.) < , >

B. On your own coordinate graph, draw any 3 or 4 sided polygon. Identify the vertices. Then translate that polygon using the vector <2, -3>. Identify the new coordinates for the vertices.

C. On a coordinate graph. Draw a triangle and list its coordinates for each vertex. Then perform 3 different translations. (Record the vector used each time). Give the final location of the triangles vertices.