Move points A, B, and C to change the shape of the triangle. Move points P and Q to move the line of reflection. Click the boxes to show segment lengths and AA', BB' and CC'.
Question 1
[i]Select the boxes for AA', BB' and CC'.[/i][br][br][b]What do you about the slope of these lines and the line of reflection, PQ?[/b]
The line segments from AA', BB' and CC' are all perpendicular to the line of reflection.
Question 2
[i]Select the box for Lengths.[/i][br][br][b]What do you notice? What is the relationship between the line of reflection and AA', BB' and CC'?[/b][br][br]
Point A to the line of reflection is the same distance as point A' to the line of reflection. Therefore, the line of reflection bisects (cuts in half) line segment AA'. Likewise for BB' and CC'.
Question 3
[i]Move point P to point A. [/i][br][br][b]How does this affect A'?[/b]
When the line of reflection (PQ) is on the point being reflected (A), the image point (A') is reflected a distance of zero, such that P, A and A' are all in the same location.
Question 4
[b]What is true about the line of reflection and line segments AA', BB' and CC'?[/b]
Question 5
[b]Write a precise definition for a rotation, using the following words or objects:[br][/b][list][*][b]Line of reflection PQ[/b][/*][*][b]Point A, not on the line PQ[/b][/*][*][b]Point B, on the line PQ[/b][/*][*][b]Line segment AA'[/b][/*][*][b]Perpendicular bisector[/b][/*][/list]
[u]BASIC DEFINITION:[/u] A reflection moves points across a specified line of reflection so that the line of reflection is the perpendicular bisector of each line segment connecting corresponding preimage and image points. [br][br][b][u]PRECISE DEFINITION:[/u] A reflection about line PQ takes each point B [i]on the line PQ [/i]to itself and each point A [i]not on the line PQ[/i] to the point A' such that PQ is the perpendicular bisector of AA'.[br][/b]
Question 6
[b]Which of the following are properties of the reflected triangle A'B'C'?[/b]