Here are the explanations for the problems shown in the image.
1. Rotations
- a) 41 turn = 90∘: This shows a shape rotated by 90∘ clockwise around its center. A quarter turn is equivalent to a 90∘ rotation.
- b) 21 turn = 180∘: This shows the same shape rotated by 180∘ clockwise around its center. A half turn is equivalent to a 180∘ rotation.
2. Look at the drawings below and explain them.
- Top left: The square is moved horizontally to the right without changing its orientation. This transformation is called a translation.
- Top right: The rectangle is turned around a fixed point (the small circle with an arrow). It has been rotated 90∘ clockwise. This transformation is called a rotation.
- Bottom left: The square is turned around a fixed point. It has been rotated 90∘ counter-clockwise. This transformation is also a rotation.
- Bottom right: The rectangle is flipped over a horizontal line (the dashed line). This transformation is called a reflection.
3. Complete the table below by rotating each shape and draw the rotated shape.
Since I cannot draw, I will describe the orientation of the rotated shapes. Assume rotations are clockwise unless specified.
-
Row 1 (Bowtie/Hourglass shape):
- Original: Two triangles joined at a point, one pointing up, one pointing down.
- 90∘ rotation: The shape will appear rotated 90∘. The top triangle will now point to the right, and the bottom triangle will point to the left.
- 180∘ rotation: The shape will look identical to the original, as it has 180∘ rotational symmetry.
- 270∘ rotation: The shape will appear rotated 270∘ clockwise (or 90∘ counter-clockwise). The top triangle will now point to the left, and the bottom triangle will point to the right.
-
Row 2 (Horizontal rectangle with a dot on the top-left corner):
- Original: A horizontal rectangle with a dot at its top-left vertex.
- 90∘ rotation: The rectangle will become vertical. The dot will be at the top-right vertex of the new vertical rectangle.
- 180∘ rotation: The rectangle will be horizontal again. The dot will be at the bottom-right vertex.
- 270∘ rotation: The rectangle will be vertical again. The dot will be at the bottom-left vertex of the new vertical rectangle.
-
Row 3 (Upright triangle with a dot on the bottom-left vertex):
- Original: An equilateral or isosceles triangle pointing upwards, with a dot at its bottom-left vertex.
- 90∘ rotation: The triangle will point to the right. The dot will be at the top vertex of the triangle.
- 180∘ rotation: The triangle will point downwards (upside-down). The dot will be at the top-right vertex.
- 270∘ rotation: The triangle will point to the left. The dot will be at the bottom vertex of the triangle.
Send me the next one 📸