To create the rest of the square design, we can use the following transformations:
1. Reflection: Reflect the shaded triangle across the y-axis to create a mirrored image on the left side of the square (Figure II).
2. Rotation: Rotate the shaded triangle 90 degrees counterclockwise around the origin to create a new triangle aligned with the positive x-axis (Figure III).
3. Translation: Move the newly rotated triangle to the top of the square by translating it vertically upward (Figure IV).
4. Reflection: Reflect the newly placed triangle across the x-axis to create a mirrored image at the bottom of the square (Figure V).
5. Rotation: Rotate the newly reflected triangle 180 degrees around the origin to create a new triangle aligned with the negative y-axis (Figure VI).
6. Translation: Move the newly rotated triangle to the left side of the square by translating it horizontally to the left (Figure VII).
7. Reflection: Reflect the newly placed triangle across the y-axis to create a mirrored image on the right side of the square (Figure VIII).
After performing these transformations, the entire square design should be complete.
Look at the shaded triangle in the drawing below. Describe in detail the transformations needed to create the rest of the square design. You can use a combination of translations, reflections, and rotations of the shaded triangle (Figure I) to create the square design.
A square is drawn on a coordinate plane with the center of the square on the origin. Two diagonals are drawn through the origin forming four congruent triangles on the inside of the square. The triangle that overlaps the positive y-axis is shaded.
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