# Lesson 3: Grid Moves

Let’s transform some figures on grids.

## 3.1: Notice and Wonder: The Isometric Grid

What do you notice? What do you wonder?

## 3.2: Transformation Information

Follow the directions below each statement to tell GeoGebra how you want the figure to move. It is important to notice that GeoGebra uses vectors to show translations. A vector is a quantity that has magnitude (size) and direction. It is usually represented by an arrow.

These applets are sensitive to clicks. Be sure to make one quick click, otherwise it may count a double-click.

After each example, click the reset button, and then move the slider over for the next question.

GeoGebra Applet Cqw7AKcp

1. Translate triangle $ABC$ so that $A$ goes to $A’$.
1. Select the Vector tool.
2. Click on the original point $A$ and then the new point $A’$. You should see a vector.
3. Select the Translate by Vector tool.
4. Click on the figure to translate, and then click on the vector.
2. Translate triangle $ABC$ so that $C$ goes to $C’$.

3. Rotate triangle $ABC$ $90^\circ$ counterclockwise using center $O$.
1. Select the Rotate around Point tool.
2. Click on the figure to rotate, and then click on the center point.
3. A dialog box will open; type the angle by which to rotate and select the direction of rotation.
4. Click on ok.
4. Reflect triangle $ABC$ using line $\ell$.
1. Select the Reflect about Line tool.
2. Click on the figure to reflect, and then click on the line of reflection.

GeoGebra Applet xbEUGnx8

1. Rotate quadrilateral $ABCD$ $60^\circ$ counterclockwise using center $B$.
2. Rotate quadrilateral $ABCD$ $60^\circ$ clockwise using center $C$.
3. Reflect quadrilateral $ABCD$ using line $\ell$.
4. Translate quadrilateral $ABCD$ so that $A$ goes to $C$.

## Summary

When a figure is on a grid, we can use the grid to describe a transformation. For example, here is a figure and an image of the figure after a move.

Quadrilateral $ABCD$ is translated 4 units to the right and 3 units down to the position of quadrilateral $A'B'C'D'$.

A second type of grid is called an isometric grid. The isometric grid is made up of equilateral triangles. The angles in the triangles all measure 60 degrees, making the isometric grid convenient for showing rotations of 60 degrees.

Here is quadrilateral $KLMN$ and its image $K'L'M'N'$ after a 60-degree counterclockwise rotation around a point $P$.