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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.

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.

7 answers

Pre-Image:

Let's create a triangle as our pre-image with the following vertices:

  • A(1, 1)
  • B(4, 1)
  • C(2.5, 3)

The coordinates of the pre-image triangle ABC are:

  • A: (1, 1)
  • B: (4, 1)
  • C: (2.5, 3)

Transformation Rules:

  1. Translation: T(x, y) -> (x + 3, y - 2)
  2. Reflection: R_x-axis: (x, y) -> (x, -y)
  3. Rotation: R(90° clockwise): (x, y) -> (y, -x)

Note: One rule is intentionally incorrect.

Applying Transformations:

  1. Translation:

    • A(1, 1) -> A'(1 + 3, 1 - 2) = A'(4, -1)
    • B(4, 1) -> B'(4 + 3, 1 - 2) = B'(7, -1)
    • C(2.5, 3) -> C'(2.5 + 3, 3 - 2) = C'(5.5, 1)

    Coordinates after Translation:

    • A': (4, -1)
    • B': (7, -1)
    • C': (5.5, 1)

  2. Reflection across the x-axis:

    • A'(4, -1) -> A''(4, 1)
    • B'(7, -1) -> B''(7, 1)
    • C'(5.5, 1) -> C''(5.5, -1)

    Coordinates after Reflection:

    • A'': (4, 1)
    • B'': (7, 1)
    • C'': (5.5, -1)

  3. Rotation (90° clockwise):

    • A''(4, 1) -> A'''(1, -4)
    • B''(7, 1) -> B'''(1, -7)
    • C''(5.5, -1) -> C'''(-1, -5.5)

    Final Image Coordinates after Rotation:

    • A''': (1, -4)
    • B''': (1, -7)
    • C''': (-1, -5.5)

Summary of Coordinates

Pre-Image Coordinates:

  • A: (1, 1)
  • B: (4, 1)
  • C: (2.5, 3)

Image Coordinates after Transformation:

  • A''': (1, -4)
  • B''': (1, -7)
  • C''': (-1, -5.5)

Drawing the Figure

Since I cannot draw directly in this format, please visualize or sketch the triangle based on the given coordinates. Once transformed, verify the new coordinates to ensure precision.

Please provide two classmates' posts for further responses!

can u make it shortter please

Sure! Here’s a more concise version:

Pre-Image (Triangle ABC):

  • A(1, 1)
  • B(4, 1)
  • C(2.5, 3)

Transformation Rules (One Incorrect):

  1. Translation: T(x, y) -> (x + 3, y - 2)
  2. Reflection: R_x-axis: (x, y) -> (x, -y)
  3. Rotation: R(90° clockwise): (x, y) -> (y, -x) (Incorrect)

Step-by-Step Transformations:

  1. Translation:

    • A': (4, -1)
    • B': (7, -1)
    • C': (5.5, 1)

  2. Reflection:

    • A'': (4, 1)
    • B'': (7, 1)
    • C'': (5.5, -1)

  3. Rotation (90° clockwise):

    • A''': (1, -4)
    • B''': (1, -7)
    • C''': (-1, -5.5)

Summary:

Pre-Image Coordinates:

  • A: (1, 1)
  • B: (4, 1)
  • C: (2.5, 3)

Image Coordinates:

  • A''': (1, -4)
  • B''': (1, -7)
  • C''': (-1, -5.5)

Feel free to ask if you need anything else!

like this for example
(2,6), (4,3), and (8,9)

Translation: Go two units ahead and six points to the left.

In a 270-clockwise rotation

Dilation: Inaccurate scale factor of 0.8

Sure, here’s the example you provided translated into a similar format for the triangle:

Coordinates:

  • A(1, 1)
  • B(4, 1)
  • C(2.5, 3)

Transformations:

  1. Translation: Move 3 units right and 2 points down.
  2. Reflection: Over the x-axis.
  3. Rotation: Incorrectly stated as 90° clockwise.

Final Coordinates:

  • Pre-Image:

    • A: (1, 1)
    • B: (4, 1)
    • C: (2.5, 3)

  • Image:

    • A''': (1, -4)
    • B''': (1, -7)
    • C''': (-1, -5.5)

Let me know if you need further modifications!

can u do it like this
ex Translation: (8,8) (1,6) (4,) (incorrect)
Reflection: 180 clockwise
Dilation: Scale factor 3

Certainly! Here’s the triangle example formatted as you requested:

Coordinates:

  • A(1, 1)
  • B(4, 1)
  • C(2.5, 3)

Transformations:

  • Translation: (4, -1), (7, -1), (5.5, 1) (Incorrect)
  • Reflection: Over the x-axis
  • Rotation: 90° clockwise (Incorrect)

Final Image Coordinates:

  • A''': (1, -4)
  • B''': (1, -7)
  • C''': (-1, -5.5)

Let me know if you need any further adjustments!