**Objective:** To understand the effects of translation on geometric
figures. To be able to make conjectures regarding geometric effects as well
as algebraic effects.

**Materials:** GSP

**Time:** 2 days

**Level of Difficulty:** Medium

**Summary of today's lesson:**

1. Using GSP, construct various polygons.

2. Find the coordinates of these figures.

3. Translate a fixed distance in a given direction.

4. Describe the effects of the translation on the coordinates of the polygon.

**Procedure:**

1. Using the segment tool go to the **Graph** menu and select **Create
axes**. Using the point on the x-axis, drag the point toward the center
until the axes have a minimum and maximum value of 10. Construct a triangle
with coordinates (1,1), (2, 6), (5, 8).

2. Each vertex of the triangle should already be labeled. (If not label.)
Highlight each vertex of the triangle, go the **Measure** menu and select
**Coordinates** to make sure you have graphed the correct coordinates.

We are also going to set the x-axis so that there is 1 centimeter in
between the origin and the adjuster point. We will first begin by checking
the preferences to see if the computer is measuring in centimeters. Go to
the **Edit** menu and click on **Preferences**. You will have to click
on the **distance unit** and drag down to centimeters. Next, measure
the distance from the origin to the adjuster point. Finally, after the measurement
is on the screen, move the adjuster point until the measurement is exactly
1 centimeter.

3. We want to translate our triangle. We can do this by giving it a fixed
distance to translate. Highlight the entire triangle by clicking and dragging
a box over the triangle. Go to the **Transform** menu and select** Translate**.
You want to click on rectangular vector. Under the horizontal section, we
are going to enter the number 5. This will translate the triangle 5 cm horizontally.
Under the vertical section, enter the number 1. This will translate the
triangle 1 cm. vertically.

4. Look at your new triangle. Find the coordinates of the new triangle. Can you see a relationship between the original coordinates and the translated triangle's coordinates? Discuss any relationships below.

5) What do you think will happen if you translate the original triangle 2 cm horizontally? Write your conjecture below. Repeat the procedures in step 3 and use 2 cm. instead of 5 cm. to see what happens. Is it what you expected?

6) How could you translate the triangle to the second quadrant? Third quadrant? Fourth quadrant? Be sure to check your guess. Label the coordinates of each translated triangle. Is there still a relationship between the original triangle's coordinates and the translated triangle's coordinates? Explain below.

7) Now you will explore with a new sketch and recreate the translation
of __any__ polygonal figure. Explain what polygonal figure you used,
how many cm. horizontally and vertically you translated, and what happened
when you translated. Check for relationships between the x and y coordinates
of each figure.