Scenario: Art & Design - Learn about transformations and symmetry through creative design projects!
You're creating a symmetrical pattern for a wallpaper design. You need to understand how to transform a basic shape to create a beautiful, balanced pattern using translations, rotations, and reflections.
Design Challenge:
Create a symmetrical pattern by transforming a triangle at (1, 1) using different transformations.
Symmetrical pattern created using transformations
Moving a shape without rotating or flipping it
Example: (x, y) → (x + 3, y + 2)
Turning a shape around a fixed point
Example: 90° clockwise around origin
Flipping a shape over a line
Example: Reflect over x-axis
Making a shape larger or smaller
Example: Scale factor of 2
A triangle has vertices at A(1, 1), B(3, 1), and C(2, 3). Translate it 4 units right and 2 units up.
Original vertices: A(1, 1), B(3, 1), C(2, 3)
Translation rule: (x, y) → (x + 4, y + 2)
New vertices: A'(5, 3), B'(7, 3), C'(6, 5)
Reflect the point P(3, 4) over the x-axis and then over the y-axis.
Original point: P(3, 4)
Reflect over x-axis: P'(3, -4)
Reflect over y-axis: P''(-3, -4)
A shape can be folded along a line and match exactly
Example: Letter "A" has vertical line symmetry
A shape looks the same after rotation
Example: Square has 4-fold rotational symmetry
Create a symmetrical logo design using transformations. Start with a simple shape and use reflections and rotations to create a balanced, professional-looking logo.
Step 1: Start with a basic shape (triangle, square, circle)
Step 2: Apply reflections to create mirror images
Step 3: Use rotations to create rotational symmetry
Result: A balanced, symmetrical logo design
Translate the point Q(2, 5) 3 units left and 4 units down.
Your solution:
Reflect the point R(4, -2) over the x-axis.
Your solution:
Create a symmetrical pattern by transforming a square at (0, 0) with side length 2. Use at least two different transformations.
Your design: