1) Translation - Geometric Transformations (Unit 5)
[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 the 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.
[justify][b]1. Translate[/b] the triangle below using two vectors: [b][i]vectors a and b[/i][/b] ,[br][br][b]2. Translate[/b] the triangle below using just the [b]vector u,[/b][br][br][b]3. Answer [/b]the questions 3, 4 and 5[br][/justify]
[justify][b]1. Translate[/b] the triangle below using two vectors: [b][i]vectors a and b[/i][/b] ,[br][br][b]2. Translate[/b] the triangle below using just the [b]vector u,[/b][br][br][b]3. Answer [/b]the questions 3, 4 and 5[br][/justify]
[justify][b]1. Translate[/b] the triangle below using two vectors: [b][i]vectors a and b[/i][/b] ,[br][br][b]2. Translate[/b] the triangle below using just the [b]vector u,[/b][br][br][b]3. Answer [/b]the questions 3, 4 and 5[br][/justify]
[justify][b]1. Translate[/b] the triangle below using two vectors: [b][i]vectors a and b[/i][/b] ,[br][br][b]2. Translate[/b] the triangle below using just the [b]vector u,[/b][br][br][b]3. Answer [/b]the questions 3, 4 and 5[br][/justify]
[b]4) Click on the box: Vector_u Components [/b]and compare the two translations using the vector a and b with the translation using the vector u. What can you conclude?
[b]5) [/b]Create a Slider to animate the motion of the given triangle in the direction of the [b]vector u=(10,2).[br][br][/b][justify][b]- Enter in [/b][url=https://www.geogebra.org/classic/meqaarxt][color=#0000ff]Geogebra link[/color][/url][b] - [/b]click on the three lines in the top right corner - save online - write your name - copy the Geogebra link and [b]paste the link in the last question of this Geogebra. [/b]If your Geogebra is in Portuguese, switch to English.[/justify][color=#980000][b]Steps:[/b][/color][b][br][br] 1. [/b]Use the triangle on the [color=#0000ff] [url=https://www.geogebra.org/classic/meqaarxt]Geogebra link[/url].[/color][b] Name it as t1[/b] ("right click" - rename) and put visible its name ("right click" - show Label),[b] 2. D[/b][b]raw the vector u=(10,2) [/b]and [b]name it as u[/b] ("right click" - rename)[b][br][br] 3. Create the Slider: [/b]Select the Slider tool and click anywhere on the Cartesian plane to create it, [b]name the slider as Vector_u[/b], and [b]select Number: Set Min: 0 and Max: 1,[br][br][/b][b]4. [/b][b] Click [/b][b]on the Input[/b][b] and write[/b][b] the command: [/b]Translate([color=#0000ff]object name[/color], [color=#4c1130]slider name[/color][b][color=#ff0000]*[/color][/b][color=#76a5af]vector name[/color]), which in this example is [b]Translate([/b][color=#0000ff]t1[/color][color=#0000ff], [/color][color=#4c1130]Vector_u[/color][b][color=#ff0000]*[/color][/b][color=#76a5af]u[/color]), and [b]click [/b]enter,[br]In this 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.[br][br][b]5. Move [/b]the slider to translate the shape in the direction of the chosen vector.[br]
[b]4) Click on the box: Vector_u Components [/b]and compare the two translations using the vector a and b with the translation using the vector u. What can you conclude?
[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]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.
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[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.