Lesson 2 Leap Frog Solidify Understanding
Given the pre-image point
A translation that will carry
A reflection that will carry
A rotation that will carry
A sequence of two transformations that will carry
Determine the rigid transformation that carries one image onto another.
When given an image and its pre-image, what do I look for to identify a rigid transformation that has already occurred?
How do I recognize when a sequence of rigid transformations may be needed to carry one figure onto another, and how do I identify what transformations that sequence might include?
How do I justify that my proposed rigid transformation, or sequence of transformations, works?
Open Up the Math: Launch, Explore, Discuss
Josh is animating a scene in which a troupe of frogs is auditioning for the Animal Channel reality show, “The Bayou’s Got Talent.” In this scene the frogs are demonstrating their “leap frog” acrobatics act. Josh has completed a few key images in this segment, and now needs to describe the transformations that connect various images in the scene.
For each pre-image/image combination listed below, describe the transformation that moves the pre-image to the final image.
If you decide the transformation is a rotation, you will need to give the center of rotation, the direction of the rotation (clockwise or counterclockwise), and the measure of the angle of rotation.
If you decide the transformation is a reflection, you will need to give the equation of the line of reflection.
If you decide the transformation is a translation, you will need to describe the “rise” and “run” between pre-image points and their corresponding image points.
If you decide it takes a combination of transformations to get from the pre-image to the final image, describe each transformation in the order they would be completed.