Transformational Geometry with Sketchpad

Transformational Geometry with Sketchpad

Translation | Rotation | Reflection | Glide Reflection

Steps for Translation

1. Construct a triangle ABC and its interior.

2. Select the points A and B and under the Transform menu, choose Mark Vector "A->B"

3. Select the interior of the triangle and under the Transform menu, choose Translate.

When the following window appears, choose By Marked Vector.

Triangle ABC was translated by the vector from A to B. The red triangle is the translated image.

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Steps for Rotation

1. Construct a triangle ABC and its interior.

2. Select one vertex of the triangle, say A, and under the Transform menu, choose Mark Center "A"

3. Select the interior of the triangle and under the Transform menu, choose Rotate.

When the following window appears, type in the number of degrees that you want to rotate the triangle.

NOTE: Both positive and negative values can be used. The positive means clockwise rotation, and the negative means counterclockwise rotation.

Triangle ABC was rotated -60^o
around the vertex A. The red triangle is the rotated image.

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Steps for Reflection

1. Construct a triangle ABC and its interior.

2. Construct a line (or line segment), which can be at any angle. Select your line (or line segment) and under the Transform menu, select Mark mirror.

3. Select the interior of the triangle and under the Transform menu, choose Reflect.

NOTE: Move your line (or line segment) around to see the effect on the reflection.

Triangle ABC was reflected over the vertical line segment. The triangle in red is the reflected image.

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Steps for Glide Reflection

Since the definition of a glide reflection is a reflection followed by a translation parallel to the fixed line of reflection, two transformations are needed here.

1. Construct a figure and construct its interior.

2. Construct a line (or line segment), which can be at any angle. Select your line (or line segment) and under the Transform menu, select Mark mirror.

3. Select the interior of the figure and under the Transform menu, choose Reflect.

4. Construct a line parallel to your original line of reflection and construct two points on it.

5. Select the two points, and under the Transform menu, select Mark Vector.

6. Select the interior of the reflected image and under the Transform menu, select Translate.

7. Again, you will be prompted with the Translate window.

8. Hide your reflected image and your parallel line.

NOTE: Move your line segment to obtain the glide reflection that you wish.

The green letter T marked with the A was reflected about the line segment to obtain the yellow letter marked with the A'. Then a parallel line to the line segment was constructed, two points, C and D were constructed on the line, and a vector from C to D was marked. Finally, the yellow letter was translated by the marked vector to obtain the final image. The letter in red is the glide reflection image.

October 31 - Tranformational Geometry