Lesson 3 Leap Frog Solidify Understanding

Jump Start

Given the pre-image point located at and the image point located at as shown in the diagram, describe the following transformations:

A translation that will carry onto

A reflection that will carry onto

A rotation that will carry onto

A sequence of two transformations that will carry onto

A coordinate plane with x- and y-axis in 1-unit increments. Point A located at (2,6) and Point A' located (6,2) x555y555000

Learning Focus

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.

1.

a coordinate plane with images of a bucket and 10 frogs x555101010151515202020252525303030y555101010151515202020252525303030000