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