Defining Translations

Move points A, B, C to change the shape of the triangle. Move point Q to change the size of vector PQ. Select or unselect 'Vectors' and 'Slope' boxes to see the vectors and slope.

Question 1

[i]Move point Q so that it is on top of point P. [/i][br][br][b]What do you notice?[/b]

Question 2

[i]Starting from (0, 0), move point Q three units left and two units up.[/i][br][br][b]What happens to A'B'C'? What is the algebraic description for this transformation.[/b]

Question 3

[b]What is true about the directed line segments AA', BB' and CC'?[/b]

They are the same length as PQ They are parallel to PQ They are the same direction as PQ

Question 4

[b]Write a precise definition for a translation, using the following words or objects:[br][/b][list][*][b]Point A[/b][/*][*][b]Point A'[/b][/*][*][b]Directed line segment PQ[/b][/*][*][b]Directed line segment AA'[/b][/*][*][b]Parallel[/b][/*][*][b]Direction[/b][/*][*][b]Length[/b][/*][/list]

Question 5

[b]Which of the following are properties of the translated triangle A'B'C'?[/b]

A'B'C' has the same orientation as ABC A'B'C' is congruent to ABC A'B'C' is similar to ABC The image line segments are parallel to the preimage line segments [i](ie, AB is parallel to A'B')[/i] The measures of angles A, B and C are preserved The lengths of segments AB, BC and AC are preserved.