Composition of Transformations Activity

[size=150]Use the checkboxes to choose 1 or 2 transformations. The decorate box can be chosen to show congruent corresponding sides. Take a moment to explore what you can do.[/size]

Questions to consider as we work through this activity.

1) Is there more than one combination of transformations that gives the same final product?[br][br]2) Does the order in which we transform the object matter?

[size=200][color=#1155cc]Task 1[br][br][/color][size=150]Use the applet below to complete the following tasks.[/size][/size]

Part 1

Translate the triangle 7 units left and 3 units down.[br]*Note: You are moving the orange point with the word drag above it.][br][br]What is the coordinate notation for this transformation?

[math]\left(x,y\right)\longrightarrow\left(x+7,y+3\right)[/math] [math]\left(x,y\right)\longrightarrow\left(x-3,y-7\right)[/math] [math]\left(x,y\right)\longrightarrow\left(x+3,y+7\right)[/math] [math]\left(x,y\right)\longrightarrow\left(x-7,y-3\right)[/math]

Part 2

Next, reflect the new triangle over the x-axis. [br]*Note: Make sure you click on the button that says "I need another transformation" first. [br][br]What is the coordinate notation for this transformation?

[math]\left(x,y\right)\longrightarrow\left(-x,y\right)[/math] [math]\left(x,y\right)\longrightarrow\left(-x,-y\right)[/math] [math]\left(x,y\right)\longrightarrow\left(y,x\right)[/math] [math]\left(x,y\right)\longrightarrow\left(x,-y\right)[/math]

Part 3

What is the coordinate notation that will take you from the original triangle to the third triangle?[br][Hint: Think about the order in which we did the transformations.]

[math]\left(x,y\right)\longrightarrow\left(x-7,-y-3\right)[/math] [math]\left(x,y\right)\longrightarrow\left(x,-y+3\right)[/math] [math]\left(x,y\right)\longrightarrow\left(x,-y-3\right)[/math] [math]\left(x,y\right)\longrightarrow\left(x-7,-y+3\right)[/math]

[color=#1155cc][size=200]Task 2[br][br][/size][/color][size=150]Use the applet below to help answer the following questions.[/size]

Question 1

[size=150]Place point A at the coordinates (3, 5). What will be the image of A be after a rotation of 90 degrees counter-clockwise followed by a translation 5 units up?[br][br][/size][size=150]Be sure to type your answer as an ordered pair.[/size]

Question 2

[size=150]Raphael and Michelangelo were both asked to use coordinate notation to describe the result of a translation 4 units left and 1 unit up, followed by a reflection across the y-axis.[br][br]Raphael wrote the following notation: (x,y) -> (-x + 4, y + 1).[br]Donatello wrote the following notation: (x,y) -> (-[x - 4], y + 1).[br][br]Who is correct?[/size]

Raphael is correct. Neither one of them is correct. Donatello is correct. They are both correct.

Question 3

Use the applet below to answer this question.[br][br]Describe the combination of transformations that could have occurred going from the gray triangle to the the pink triangle.

Rotation 180 degrees about the origin followed by a translation up 1 unit. Reflect across the line x = 1 and translate down 4 units. Reflect across the line y = x, then translate up 2 units. Reflection across the y-axis followed by a translation down 4 units.

Question 4

[size=150]Is there another way to get the same transformation to happen as in question 3? If so, explain your sequence of transformations.[br][br][/size][size=150]Use the applet below to explore.[/size]