## TRANSLATION CHALLENGES—THE TRANSLATION FAMILY

Prerequisites:

In Geometric Functions activities students create, manipulate, and experience function concepts by treating geometric transformations as functions with points as their variables.

Students explore translations as functions. They construct a translation function, label the variables using function notation, and trace the variables to compare their paths. They restrict the domain to reveal the corresponding range, and they change the translation vector to create different members of the translation family. Finally, students solve translation challenges by figuring out the vector to match an existing translation.

OBJECTIVES

In this activity students will:

• Construct an independent variable point x and translate it by a polar vector.
• Label the dependent variable using function notation.
• Drag the independent variable while tracing both variables, and describe the variables’ relative motion (their covariation) and the relationship between their traces (their correspondence).
• Translate an independent point using a polar vector defined by a distance parameter and an angle parameter.
• Adjust the parameters to create different members of the translation family.
• Restrict the domain of the independent variable to the border of a polygon, and observe and describe the resulting range by dragging the independent variable.
• Identify any fixed points of the function, and explicitly compare the relative motion (both speed and direction) of the independent and dependent variables.
• Solve challenges that involve finding a translation vector in polar, rectangular, or two-point form given an object and its translated image.

COMMON CORE CONNECTIONS
Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to precision; (7) Look for and make use of structure; (8) Look for and express regularity in repeated reasoning.

Content Standards

8.F1,2; 8.G1; F-IF1,2,9; G-CO2; G-SRT1