Reflections, Translations and Grids
- Arpit Kesharwani
1.5 Coordinate MovesUNIT 1 • LESSON 5 COORDINATE MOVES
WHAT YOU WILL LEARNIn this lesson, I will transform some figures and see what happens to the coordinates of points.I can...
I will know I learned by...
FAMILY MATERIALS:To review or build a deeper understanding of the math concepts, skills, and practices in this lesson, visit the Family Materials provided by Illustrative Mathematics Open-Up Resources. (Links to an external site.)Links to an external site.Select all of the translations that take Triangle T to Triangle U. There may be more than one correct answer.
The applet has instructions for the first 3 questions built into it. Move the slider marked “question” when you are ready to answer the next one. Pause before using the applet to show the transformation described in each question to predict where the new coordinates will be.Apply each of the following transformations to segment ABAB. Use the Pen tool to record the coordinates.
Geogebra Applet (Links to an external site.)Links to an external site.Suppose EFEF and GHGH are line segments of the same length. Describe a sequence of transformations that moves EFEF to GHGH.We can use coordinates to describe points and find patterns in the coordinates of transformed points.We can describe a translation by expressing it as a sequence of horizontal and vertical translations. For example, segment AB is translated right 3 and down 2.
Reflecting a point across an axis changes the sign of one coordinate. For example, reflecting the point A whose coordinates are (2,-1) across the x-axis changes the sign of the y-coordinate, making its image the point A′ whose coordinates are (2,1). Reflecting the point A across the y-axis changes the sign of the x-coordinate, making the image the point A″ whose coordinates are (-2,-1).
Reflections across other lines are more complex to describe.We don’t have the tools yet to describe rotations in terms of coordinates in general. Here is an example of a 90∘ rotation with center (0,0) in a counterclockwise direction.
Point A has coordinates (0,0). Segment AB was rotated 90∘ counterclockwise around A. Point B with coordinates (2,3) rotates to point B′ whose coordinates are (-3,2). All Illustrative Mathematics Open Up Resources can be Downloaded for free at openupresources.org (Links to an external site.)Links to an external site.. Any additional HCPSS content is offered under a CC Attribution Non-Commercial Share AlikeLinks to an external site. license.