Question

lesson 2: leap frog
ready, set, go

ready

in each problem, there will be a pre - image and several images based on the given pre - image.
determine which of the images are rotations of the given pre - image and which of them are
reflections of the pre - image. if an image is the result of a rotation and a reflection, then state both.
(compare all images to the pre - image.)

1. \ta. \tb.

\tc. \td.

1. \ta. \tb.

\tc. \td.

Explanation:

To solve these problems, we analyze each image relative to the pre - image by recalling the definitions of rotation and reflection:

Problem 1

• Pre - image: A rectangle with a dot in the upper - right - side interior.
• Image a:
• The rectangle is rotated 90 degrees counter - clockwise (or 270 degrees clockwise) and also reflected (the position of the dot relative to the rectangle's orientation suggests a reflection). So, it is a result of both rotation and reflection.
• Image b:
• The rectangle is rotated 90 degrees clockwise (or 270 degrees counter - clockwise) and reflected. The orientation of the rectangle and the position of the dot indicate both transformation types. So, it is a result of both rotation and reflection.
• Image c:
• The rectangle is rotated 180 degrees (either clockwise or counter - clockwise). The overall orientation and the position of the dot relative to the pre - image are consistent with a 180 - degree rotation. So, it is a rotation.
• Image d:
• The rectangle is reflected (across a vertical or horizontal axis, depending on the orientation) and rotated. The new orientation of the rectangle and the dot's position imply both reflection and rotation. So, it is a result of both rotation and reflection.

Problem 2

• Pre - image: A triangle with a specific orientation (let's say with a tall, narrow shape and a vertex at the top).
• Image a:
• The triangle is reflected (across a vertical axis, for example). The mirror - image - like quality of the triangle's shape relative to the pre - image indicates a reflection.
• Image b:
• The triangle is rotated (probably 90 degrees or 180 degrees, depending on the exact orientation change). The change in the triangle's orientation from the pre - image suggests a rotation.
• Image c:
• The triangle is rotated (maybe 180 degrees or a different angle that changes its orientation significantly). The new position of the vertices relative to the pre - image shows a rotation.
• Image d:
• The triangle is reflected (across a horizontal or vertical axis) and rotated. The combined change in shape orientation and vertex positions implies both reflection and rotation.

Final Answers (for each sub - problem)

Problem 1

• a: Rotation and Reflection
• b: Rotation and Reflection
• c: Rotation
• d: Rotation and Reflection

Problem 2

• a: Reflection
• b: Rotation
• c: Rotation
• d: Rotation and Reflection

Answer:

To solve these problems, we analyze each image relative to the pre - image by recalling the definitions of rotation and reflection:

Problem 1

• Pre - image: A rectangle with a dot in the upper - right - side interior.
• Image a:
• The rectangle is rotated 90 degrees counter - clockwise (or 270 degrees clockwise) and also reflected (the position of the dot relative to the rectangle's orientation suggests a reflection). So, it is a result of both rotation and reflection.
• Image b:
• The rectangle is rotated 90 degrees clockwise (or 270 degrees counter - clockwise) and reflected. The orientation of the rectangle and the position of the dot indicate both transformation types. So, it is a result of both rotation and reflection.
• Image c:
• The rectangle is rotated 180 degrees (either clockwise or counter - clockwise). The overall orientation and the position of the dot relative to the pre - image are consistent with a 180 - degree rotation. So, it is a rotation.
• Image d:
• The rectangle is reflected (across a vertical or horizontal axis, depending on the orientation) and rotated. The new orientation of the rectangle and the dot's position imply both reflection and rotation. So, it is a result of both rotation and reflection.

Problem 2

• Pre - image: A triangle with a specific orientation (let's say with a tall, narrow shape and a vertex at the top).
• Image a:
• The triangle is reflected (across a vertical axis, for example). The mirror - image - like quality of the triangle's shape relative to the pre - image indicates a reflection.
• Image b:
• The triangle is rotated (probably 90 degrees or 180 degrees, depending on the exact orientation change). The change in the triangle's orientation from the pre - image suggests a rotation.
• Image c:
• The triangle is rotated (maybe 180 degrees or a different angle that changes its orientation significantly). The new position of the vertices relative to the pre - image shows a rotation.
• Image d:
• The triangle is reflected (across a horizontal or vertical axis) and rotated. The combined change in shape orientation and vertex positions implies both reflection and rotation.

Final Answers (for each sub - problem)

Problem 1

• a: Rotation and Reflection
• b: Rotation and Reflection
• c: Rotation
• d: Rotation and Reflection

Problem 2

• a: Reflection
• b: Rotation
• c: Rotation
• d: Rotation and Reflection