W. Gary Martin home page > CTSE 7970 > Lab 7
Lab 7 – Geometer’s Sketchpad IV (Transformations)
1. TRANSLATIONS.
a. Draw a triangle. Then select it. Under Transform, select “Translate…” Specify an angle and location. Reshape your original triangle and notice what happens! Also, more your triangle around and note the results.
b. Now highlight your triangle again and specify By Rectangular Vector…
c. Finally, we get to the most powerful method. Draw a segment and then select both its endpoints. Under Transform, select Mark Vector. Highlight your triangle again. Then under Transform, select Translate… by Marked vector. Move the endpoints of your segment and observe what happens.
2. REFLECTIONS.
a. Draw a line. Highlight the line. Then under Transform, choose Mark Mirror.
b. Again select your triangle. Then under Transform, choose “Reflect”. Move your triangle around and note what happens. Move the line around and note what happens.
c. Move the line so it goes through the triangle. What happens?
d. More the reflection line so that it goes through your triangle. Move the vertices of the triangle so that its reflection exactly ends up on top of the figure. What do we call such a figure?
e. Draw a quadrilateral and repeat (c).
3. ROTATIONS.
a. Draw a point and select it. Then under Transform, select Mark Center…
b. Select your triangle. Then choose Rotate under the Transform menu. Enter an angle. Move the pre-image around and see what happens! Move the center point around as well.
c. Rotate a triangle 180 degrees around the midpoint of each of its sides to make an interesting pattern. Make several observations.
d. Now we’ll use a variable angle. Draw an angle (two segments with a common endpoint will suffice). Now highlight the three points that determine the angle and under Transform, select Mark Angle. Now highlight your triangle and go under the Transform menu and choose Rotate… by Marked Angle. Then adjust your angle and observe what happens.
e. Move the center point of a rotation inside of a triangle that is being rotated. What do you observe? Now reshape the triangle so that it exactly fits on top of itself. (You may also have to adjust the angle. What do we call such figures?)
f. Draw a quadrilateral and repeat part (c).
4. DILATING.
a. Draw a point and select it. Then under Transform, select Mark Center…
b. Select your triangle. Then choose Dilate under the Transform menu. Enter values for the ratio. Move the pre-image around and see what happens! Move the center point around as well.
c. Make a “spider web” like this:
Make several observations.
d. Finally, we can create a varying scale factor. Draw two segments. Click on one then the other. Under Transform, choose Mark Ratio. Then highlight your triangle and choose Dilate under transform. Move the triangle, center, and two segments around to see what is happening. How are the two triangles related? How can you make one smaller than the other? Bigger?
5. COMPOSITIONS.
a. Reflect a triangle over one line. Draw a second line and reflect the image (A’B’C’) of the first reflection over that line.
b. How are the two triangles related?
c. Move the lines around to see if you can find a different relationship.
d. Let’s define this composition: Choose a segment of the original pre-image and the corresponding side of the final image. Under Transform, choose Define Transformation. Enter some appropriate name… You can now transform other objects using this combination of reflections.
e. Now define a transformation (see part (d)) using two lines that meet at a common point – that is, draw the second line using one of the points of your first line.
f. Now find a SINGLE transformation (e.g., translation, rotation, etc.) that will take the pre-image to the final image. Move your figures around to see if you really have the right relationship!
g. Measure various angles (using the center point of the rotation) and distances. Make one or more conclusions…
h. Draw two parallel lines and repeat (f) and (g).