Answer this in grade 11 level: Composition of Transformations - Discussion Assignment

Question

To complete this discussion assignment, you must perform a composition transformation on a shape of your choice. Remember, a “composition” is simply a combination of two or more transformations (i.e. translation, reflection, rotation, or dilation). Here are the steps you must complete to earn full credit:

Select a shape, then describe the initial coordinates of your shape. For instance, I am choosing a square with coordinates A(-4,4), B(-2,4), C(-4,2), and D(-2,2). Scroll down to page 2 to see what this looks like.
Choose a composition transformation and then describe it in writing (example: “I will be doing a composition transformation with two steps: a translation to the right by eight units, followed by a reflection across the x-axis”).
Provide the algebraic instructions for your composition transformation. For example, the composition described above would be (x,y)(x+8,y) for the translation, and (x,y)(x,-y) for the reflection. I recommend graphing your transformations (either on paper, or using an online tool such as Geogebra).
Remember to reply to at least two posts of your classmates. Comment on something that they did well in their transformations, or offer a suggestion about another type of transformation that they could use instead. Please be positive and constructive.

Answer 1

Composition of Transformations - Discussion Assignment

Step 1: Select a Shape

I have chosen a triangle with the following coordinates:

• A(1, 2)
• B(4, 2)
• C(2.5, 5)

This triangle is located in the first quadrant of the coordinate plane.

Step 2: Describe the Composition Transformation

I will be performing a composition transformation with two steps:

1. A translation upwards by 3 units.
2. A reflection across the y-axis.

Step 3: Algebraic Instructions for the Composition Transformation

1. Translation upwards by 3 units:
   The algebraic instruction for this transformation will be:
   \[(x, y) \to (x, y + 3)\]

2. Reflection across the y-axis:
   The algebraic instruction for this transformation will be:
   \[(x, y) \to (-x, y)\]

Putting It All Together:

We first apply the translation and then the reflection. So, starting from the original coordinates of the triangle:

1. After Translation:

• A(1, 2) → A'(1, 2 + 3) = A'(1, 5)

• B(4, 2) → B'(4, 2 + 3) = B'(4, 5)

• C(2.5, 5) → C'(2.5, 5 + 3) = C'(2.5, 8)

  Coordinates after translation are: A'(1, 5), B'(4, 5), C'(2.5, 8).

2. After Reflection:

• A'(1, 5) → A''(-1, 5)

• B'(4, 5) → B''(-4, 5)

• C'(2.5, 8) → C''(-2.5, 8)

  Final coordinates after reflection are: A''(-1, 5), B''(-4, 5), C''(-2.5, 8).

Conclusion

The composition of transformations has resulted in the triangle being translated upwards by 3 units and then reflected across the y-axis. The final coordinates of the triangle are A''(-1, 5), B''(-4, 5), and C''(-2.5, 8).

I'll graph these transformations to visually see the changes. Looking forward to seeing everyone else's transformations!