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.[br][br]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.
Translation[br][list][*]perpendicular to the parallel lines[/*][*]towards the parallel lines[/*][*][u]twice[/u] the distance between the parallel lines[/*][/list]
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.[br][br]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.
Translation[br][list][*]perpendicular to the parallel lines[/*][*]towards the parallel lines[/*][*][u]twice[/u] the distance between the parallel lines[/*][/list]
Make a conjecture:[br]If a pre-image is reflected across one of two parallel lines, then that image is reflected across the other line...
The resulting image is equivalent to one translation perpendicular to and [u]towards[/u] the parallel lines.[br]The distance of the translation is twice the distance between the parallel lines.
Does it matter if the first reflection line is the line further from the pre-image?
Yes, it does matter. [br]If completed in this order, the resulting image is equivalent to one translation perpendicular to and [u]away from[/u] the parallel lines. [br]The distance of the translation remains twice the distance between the parallel lines.
The illustration below shows a figure and two intersecting lines, [i]m[/i] and [i]p[/i].[br][br]Reflect the arrow across line [i]m[/i]. Then reflect that image across line [i]p[/i].
What single transformation produces the same image as the two reflections? Your description should include a measurement.
Rotation of 90º clockwise about the point of intersection of the two lines.[br]
The illustration below shows a figure and two intersecting lines, [i]n[/i] and [i]s[/i].[br][br]Reflect the figure across line [i]n[/i]. Then reflect that image across line [i]s[/i].
What single transformation produces the same image as the two reflections? Your description should include a measurement.
A rotation of 180º clockwise about the point of intersection of the two lines.
Make a conjecture:[br]If a figure is reflected across one of two intersecting lines, then that image is reflected across the other line...
The resulting image is a rotation about the point of intersection of the two lines. The angle of rotation is twice the measure of the angle formed by the intersecting lines.