Lesson 2: 3-2: Translations

1. What lets you know the magnitude and direction of a translation?
2. How does a coordinate plane help to check the translation of an image?
3. What notation is used to simplify discussion of translations?

Translation Vector

G.CO.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.5
Given a geometric figure and a rotation, reflections, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.

A translation is a transformation that moves all points of a figure the same distance in the same direction.Translations on the coordinate plane can be drawn using the translation vector. One way to translate a figure in the coordinate plane is simply to count units on the x-axis and on the y-axis.
Mathematically proficient students consider the available tools when solving a mathematical problem.

Stop-motion animation is a technique in which an object is moved by very small amounts between individually photographed frames. When the series of frames is played as a continuous sequence, the result is the illusion of movement.

When translating a point along a vector, students should be careful of the signs of the coordinate of the point and the vector.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher. Students can also be given poster board sized coordinate grids and laminated shapes to physically translate the objects.
Students beyond grade level can make deeper connections in the following way: students can look at an image that has been translated multiple times and determine the one vector that will translate the original image to the final image.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.