4.3 Transformations

• Rotation turns a shape around a fixed point by a specified angle.


  True
• Translation moves a shape without changing its size, shape, or orientation.

  True
• What is the fixed point called around which a rotation occurs?

  Center of rotation
• Transformations can be described using coordinates, vectors, and angles.

  True
• A rotation turns a shape around a fixed point
• Match the transformation type with its definition:

  Translation ↔️ Moves a shape without changing size or orientation

  Rotation ↔️ Turns a shape around a fixed point

  Reflection ↔️ Flips a shape over a line

  Enlargement ↔️ Changes the size of a shape
• The fixed point around which a rotation occurs is called the center
• Reflecting a shape over the line y = x flips it across the line
• If a triangle is enlarged by a scale factor of 2, how does its size change?

  It doubles
• Translating a triangle by the vector $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$ moves each vertex 3 units to the right and 2 units up.


  True
• Rotating a point (1, 2) 90° counterclockwise around the origin results in (-2, 1).

  True
• Reflecting a triangle over the line y = x changes its orientation but preserves its size and shape.


  True
• The order of transformations affects the final result of combining them.
• Transformations are changes made to the position, size, or orientation of a shape
• Transformations can be described using mathematical language and notation, such as coordinates, vectors, and angles
• Arrange the transformations based on whether they change orientation.

  1️⃣ Translation

  2️⃣ Enlargement

  3️⃣ Rotation

  4️⃣ Reflection
• Enlargement is a transformation that changes the size
• Which transformation creates a mirror image of a shape?

  Reflection
• What does the transformation called 'translation' do to a shape?

  Moves it to a new position
• An enlargement changes the orientation of a shape.

  False
• What happens to the orientation of a shape after a rotation?

  It changes
• What are the two possible directions of rotation?

  Clockwise and counterclockwise
• An enlargement changes the orientation of a shape.

  False
• What is a translation in geometric transformations?

  Movement without altering size
• Rotation involves turning a shape around a fixed point by a specified angle of rotation.
• A reflection creates a mirror image of a shape across a specified line.
• The combined transformation matrix for a translation followed by a 90° counterclockwise rotation is $\begin{pmatrix} 0 & - 1 \\ 1 & 0 \end{pmatrix}$.


  True
• What are transformations in geometry?

  Changes to position, size, orientation
• Which transformation changes the size of a shape while keeping its orientation?

  Enlargement
• What does the vector \begin{pmatrix} 3 \\ 2 \end{pmatrix}</latex> represent in a translation?

  Movement 3 right, 2 up
• Reflection flips a shape over a line to create a mirror image.

  True
• How is a translation described mathematically?

  Coordinates and vectors
• What is the result of reflecting a shape over a line?

  A mirror image
• Steps for representing a translation using a vector:

  1️⃣ Identify the direction and distance of movement

  2️⃣ Write the vector in component form

  3️⃣ Apply the vector to each vertex of the shape

  4️⃣ Draw the new shape at its translated position
• A rotation changes the size of a shape.

  False
• What is used to describe the change in size during an enlargement?

  A scale factor
• Steps for applying a translation using a vector:

  1️⃣ Determine the vector components

  2️⃣ Add the vector components to the coordinates of each vertex

  3️⃣ Plot the new vertices

  4️⃣ Draw the translated shape
• What is the fixed point around which a shape rotates called?

  Center of rotation
• What is a reflection in geometric transformations?

  Flipping over a line
• What determines how much a shape is scaled up or down in an enlargement?

  Scale factor