Math 8 Unit 1 Lesson 5: Coordinate Moves

Author:Lindsay Rice, IM 6 – 8 Math, GeoGebra Classroom Activities

Adapted from Open Up Resources https://openupresources.org/

Select all of the translations that take Triangle T to Triangle U. There may be more than one correct answer.

Select all that apply

A
Translate to .
B
Translate to .
C
Translate to .
D
Translate to .

Five points are plotted on the coordinate plane.

Using the Pen tool or the Text tool, label each with its coordinates.
Using the -axis as the line of reflection, plot the image of each point.
Label the image of each point with its coordinates.
Include a label using a letter. For example, the image of point should be labeled .

If the point were reflected using the -axis as the line of reflection, what would be coordinates of the image? What about ? ? Explain how you know.

The point R has coordinates (3,2).

Without graphing, predict the coordinates of the image of point if point were reflected using the -axis as the line of reflection.

Check your answer by finding the image of R on the graph. Label the image of point R as R' using the Text or Pen tool.

What are the coordinates of ?

Suppose you reflect a point using the -axis as line of reflection. How would you describe its image?

Apply each of the following transformations to segment AB using the applet that follows. Use the Pen tool to record the coordinates.

In the applet below, rotate segment 90 degrees counterclockwise around center by moving the slider marked 0 degrees. The image of is named . What are the coordinates of ?

In the applet below, rotate segment 90 degrees clockwise around by moving the slider marked 0 degrees. The image of is named and the image of is named . What are the coordinates of and ?

Compare the two 90-degree counterclockwise rotations of segment . What is the same about the images of these rotations? What is different?

Are you ready for more?

Suppose and are line segments of the same length. Describe a sequence of transformations that moves to .

Lesson 5 Summary

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

rotation with center (0,0) in a counterclockwise direction.

Point A has coordinates (0,0). Segment AB was rotated

counterclockwise around A. Point B with coordinates (2,3) rotates to point B' whose coordinates are (-3, 2).

Lesson 5 Cool Down: Rotation or Reflection

One of the triangles pictured is a rotation of triangle and one of them is a reflection. Identify the center of rotation, and label the rotated image PQR.

Identify the line of reflection, and label the reflected image .