Draw a figure with 3-5 sides. Label each vertex. Perform a composition transformation on your pre-image. Be sure to make note of vertex coordinates at each step. In discussion give the coordinates of your pre-image and image. (You may include a picture of the pre-image & image). You may also post your transformation rules, but one rule must be incorrect.

Question

After you have posted your coordinates and rules, respond to two of your classmates' posts. In your response to each post:

Write the correct transformation rules for the image coordinates given by a classmate.
Find the correct coordinates for the transformation rules your classmate gave.

Pre-image coordinates
Image coordinates
Reflection
Translation

Answer 1

Pre-image of a Triangle

Let's start by drawing a triangle (a 3-sided polygon) with the following vertex coordinates:

• Vertex A: (1, 1)
• Vertex B: (4, 1)
• Vertex C: (2.5, 4)

Pre-image Coordinates

• A (1, 1)
• B (4, 1)
• C (2.5, 4)

Composition Transformation

For this composition, I will perform the following transformations:

1. Reflection across the x-axis
2. Translation by (3, -2)

Transformation Steps

1. Reflection across the x-axis:

   • The reflection rule is given by (x, y) -> (x, -y).
   • Applying this rule:
     • A' = (1, -1)
     • B' = (4, -1)
     • C' = (2.5, -4)

   Coordinates after reflection:

   • A' (1, -1)
   • B' (4, -1)
   • C' (2.5, -4)

2. Translation by (3, -2):

   • The translation rule is given by (x, y) -> (x + 3, y - 2).
   • Applying this rule:
     • A'' = (1 + 3, -1 - 2) = (4, -3)
     • B'' = (4 + 3, -1 - 2) = (7, -3)
     • C'' = (2.5 + 3, -4 - 2) = (5.5, -6)

   Image Coordinates:

   • A'' (4, -3)
   • B'' (7, -3)
   • C'' (5.5, -6)

Summary of the Transformation

• Pre-image coordinates:
  • A (1, 1), B (4, 1), C (2.5, 4)
• Image coordinates:
  • A'' (4, -3), B'' (7, -3), C'' (5.5, -6)

Transformation Rules (Include at least one incorrect)

1. Reflection across the x-axis: (x, y) -> (x, -y) (correct)
2. Translation by (3, -2): (x, y) -> (x + 3, y - 2) (incorrect should be +3, -1)

Visual Representation

(You can sketch the triangle with the pre-image and image coordinates labeled accordingly.)

Note: Make sure to validate the transformation rules and their effects when responding to classmates!