1) Translation - Geometric Transformations (Unit 4)
[justify]Geogebra uses vectors to show translations. A [i]vector[/i] is a quantity that has magnitude (size) and direction. It is represented by a directed line segment, a segment with an arrow at one end indicating the direction of movement that has a specific length. [/justify][br][b]Translate[/b] the triangle below using the [b][i]vector u[/i][/b] and then answer the following questions.[br][br]
Instructions:
[b]1)[/b] Complete the statements below. Write as 6 answers in order using a comma to separate them[br][br]- To translate a shape you need to move the shape to a new _____________,[br][br]- The triangle __________ is the image of the triangle ABC under a translation,[br][br]- The directions of the the translation was given in terms of the __________ u,[br][br]- The distance between the points: A and A’ is _________; B and B’ is _________ and C and C’ is ________
[b]2)[/b] Describe the movement of the original triangle to its image using the previous statements. Indicate the units and direction.
[b]3)[/b] To move a shape to a new position we can use one or more translations. Describe the movement of the original triangle to its image using two translations.
[b]4) Click on the box: Vector_u Components [/b]and compare the two translations you used in the last question with the vector u. What can you conclude?
[b]5) [/b]Create a Slider to animate the motion of the triangle in the direction of the [b]vector u.[br][br]Instructions:[br][br]- Select the Slider tool [/b]and click anywhere on the Cartesian plane[b]. [br]- Name it [/b]as Vector_u and[b] select Number: Set [/b]Min: 0[b] and [/b]Max: 1[b]. [br]- Click [/b][b]on the Input[/b][b] and write[/b][b] the command: T[/b][b]ranslate(t1, Vector_u*u) [/b]and [b]click [/b]enter,[br][b]- [/b][b]Move [/b]the slider to translate the shape in the direction of the chosen vector.[justify][b][br]Observations: [/b]In the command Translate(t1, Vector_u*u), t1 is the shape we are going to translate, Vector_u is the name of the slider, * is the multiplication operation and u is the vector we will use to translate the shape.[/justify]
[b]6) [/b]Assume that the vector is v= (-10, 2) instead of u= (10, 2). [br][br] [b]a) [/b]Draw this vector v in Geogebra and translate the original triangle using it. [br][br][b] b)[/b] Create a Slider to animate the motion of the triangle in the direction of the vector v.[br][br][b] c) [/b] What does this translation with [b]vector v[/b] differ from that performed with [b]vector u?[/b]
[b]7)[/b] Assume that the vector is [b]p= (10, -2)[/b] instead of [b]u= (10, 2). [/b][br][br][b] a)[/b] Draw this vector in Geogebra and translate the[br]triangle using it.[br][br] [b] b)[/b] Create a [b]Slider [/b]to animate the motion of the triangle in the direction of the [b]vector p.[br][br][/b][b] c) [/b][b] [/b]What does this translation with[b] vector p [/b]differ from that performed with [b]vector u.[/b]
[b]8)[/b] Assume that the vector is [b]f= (-10,-2)[/b] instead of [b]u= (10, 2).[/b][br][br][b] a)[/b] Draw this vector in Geogebra and translate the triangle using it[br][br][b] b) [/b]Create a [b]Slider [/b]to animate the motion of the triangle in the direction of the [b]vector f[/b][b].[/b][br][br][b] c) [/b] What does this translation with [b]vector f[/b] differ from that performed with [b]vector u?[/b][br]
[b]9)[/b] Create a shape with more than three vertices and a [b]vector z [/b]in the diagonal position. Then move the shape through this [b]vector z.[/b][br][br][br][b]a)[/b] Describe the movement of your shape using one translation.[br][br][b]b)[/b] Describe the movement of your shape using two translations.