GeoGebra Classroom

# Multiple Transformations

## Number 1

On the grid below, draw a pair of vertical lines on the same side of A. They can be any number of units apart, but keep track of how far apart they are. Reflect A across the line closer to point A to produce image A'. Then reflect A' across the other line to produce image A".

What single transformation produces image A" from pre-image A? Your description should include a measurement.

## Number 2

On the grid below, draw another pair of parallel lines on the same side of B. Make the distance between the parallel lines different than the lines you drew in Number 1. Reflect B across the line closer to point B to produce image B'. Then reflect B' across the other line to produce image B".

What single transformation produces image B" from pre-image B? Your description should include a measurement.

Make a conjecture: If a pre-image is reflected across one of two parallel lines, then that image is reflected across the other line...

Does it matter if the first reflection line is the line further from the pre-image?

## Number 3

The illustration below shows a figure and two intersecting lines, m and p. Reflect the arrow across line m. Then reflect that image across line p.

What single transformation produces the same image as the two reflections? Your description should include a measurement.

## Number 4

The illustration below shows a figure and two intersecting lines, n and s. Reflect the figure across line n. Then reflect that image across line s.

What single transformation produces the same image as the two reflections? Your description should include a measurement.

Make a conjecture: If a figure is reflected across one of two intersecting lines, then that image is reflected across the other line...