# Lesson 5Coordinate Moves

Let’s transform some figures and see what happens to the coordinates of points.

### Learning Targets:

• I can apply transformations to points on a grid if I know their coordinates.

## 5.1Translating Coordinates

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

1. Translate to .
2. Translate to .
3. Translate to .
4. Translate to .

## 5.2Reflecting Points on the Coordinate Plane

1. Five points are plotted on the coordinate plane.

1. Using the Pen tool or the Text tool, label each with its coordinates.

2. Using the -axis as the line of reflection, plot the image of each point.

3. Label the image of each point using a letter. For example, the image of point should be labeled .

4. Label each with its coordinates.

2. 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.

3. The point has coordinates .

1. Without graphing, predict the coordinates of the image of point if point were reflected using the -axis as the line of reflection.
2. Check your answer by finding the image of on the graph.

3. Label the image of point as .

4. What are the coordinates of ?

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

## 5.3Transformations of a Segment

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 . Use the Pen tool to record the coordinates.

1. Rotate segment 90 degrees counterclockwise around center by moving the slider marked 0 degrees. The image of is named . What are the coordinates of ?

2. Rotate segment 90 degrees counterclockwise around center by moving the slider marked 0 degrees. The image of is named . What are the coordinates of ?

3. 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 ?

4. 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 is translated right 3 and down 2.

Reflecting a point across an axis changes the sign of one coordinate. For example, reflecting the point whose coordinates are across the -axis changes the sign of the -coordinate, making its image the point whose coordinates are . Reflecting the point across the -axis changes the sign of the -coordinate, making the image the point whose coordinates are .

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 in a counterclockwise direction.

Point has coordinates . Segment was rotated counterclockwise around . Point with coordinates rotates to point whose coordinates are .

## Lesson 5 Practice Problems

1. Here are some points.

What are the coordinates of , , and after a translation to the right by 4 units and up 1 unit? Plot these points on the grid, and label them , and .

2. Here are some points.

What are the coordinates of , , and after a reflection over the -axis? Plot these points on the grid, and label them , and .

3. Here are some points.

What are the coordinates of , , and after a rotation about by 90 degrees clockwise? Plot these points on the grid, and label them , and .

1. Describe a sequence of transformations that takes trapezoid A to trapezoid B.

2. Reflect polygon using line .