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GeoGebraGeoGebra Classroom

Composition of Transformations Lab

Author:
Mr. Pierce

For the following example:

I have translated triangle(ABC) by the vector defined by (20,0) to get the image triangle(A'B'C'). I have given you two parallel lines, f and g. - Reflect triangle(ABC) over line f. - Now reflect the image from the previous reflection over line g. What do you notice about the orientation of the image after two reflections? - Let's see if we can map the image from two reflections onto triangle(A'B'C'). Adjust the endpoints of the vector so that triangle(A'B'C') maps onto the image after two reflections. - Measure the distance between lines f and g. How does that relate to the length of the vector? (use your measure tool)

Translation

For the following example:

In the following worksheet, I have rotated triangle(ABC) about point D counterclockwise. This time the lines of reflection were not parallel. - Using your rules of rotation, what angle did I rotate triangle(ABC) to get triangle(A'B'C')? - Reflect triangle(ABC) over line f. - Now reflect the image from the previous reflection over line g. - Rotate line g (by moving point F) so that triangle(GHI) maps back onto triangle(ABC). What is the relationship between lines f and g? - Now rotate the line g so that the image after two reflections maps to triangle(A'B'C'). Find the angle between lines f and g. How does that relate to the angle of rotation from triangle(ABC) to triangle(A'B'C')? - What is the relationship between the point of rotation and the intersection of lines f and g?

Rotation