Activity #1

The Product of Reflections Part I

Solutions

In this activity you are going to investigate the product of motions in the plane.

1. Reflect Triangle ABC over line m and label it Triangle A’B’C’. Then reflect Triangle A’B’C’ over line n and label it Triangle A’’B’’C’’. One member of the group use a MIRA; one member should use tracing paper (or patty paper); and the third should simulate the drawing on GSP. (Note: ).

Now answer the following questions.

a) What single transformation will take DABC to DA’’B’’C’’? Translation

b) Measure the distance between the two parallel lines. (cm) 5 cm

c) Measure the distance from point A to point A’’, B to B”, and C to C”. (cm) 10 cm

d) What conjectures can you draw about the reflection of an object over two parallel lines? If you reflect over two parallel lines, the resulting transformation is a translation.

e) Would the result be the same if you reflected first over line n and then over line m? No How will it differ? Opposite direction

2) Reflect Triangle ABC over line m and label it Triangle A’B’C’. Then reflect Triangle A’B’C’ over line n and label the resulting Triangle A’’B’’C’’. One member of the group use a MIRA; one member should use tracing paper (or patty paper); and the third should simulate the drawing on GSP.

Now answer the following questions.

a) What single transformation will take DABC to DA’’B’’C’’? Rotation

b) Measure the angle between the two intersecting lines with a protractor or the Measure Tool on GSP. (Ð DOG) about 65°

c) Measure the angle COC’’, AOA’”, and BOB” about 130°

d) What conjecture can you draw about the reflection of an object over two intersecting lines? If an object is reflected over two intersecting lines, the resulting transformation is a rotation.

Activity #1

The Product of Reflections Part II

Using the product of two reflections and a MIRA only, translate DABC by vector v. Refer back to Activity #1 (completed in class) if necessary. Must construct two parallel lines perpendicular to the vector – one at the midpoint and one at the end.

Using the product of two reflections and a MIRA and a protractor, rotate DABC about point O -60°. Refer back to previous activity sheet if necessary. Must construct a 30° angle at O with 2 intersecting lines

· O