Question

dakota has a mirror in the shape of a trapezoid. she started by hanging the mirror in one location. then she decided to hang the mirror in a different location. a. complete the drawing of the mirror in its new location. b. how could dakota move the mirror from the first location to the second location? c. how have the parallel sides of the mirror changed? d. describe how the side lengths and angle measures were affected when dakota moved the mirror. how do you know? check understanding 1. darby hung a kite on the wall. then she slid the kite higher on the wall to a better position. what is true about the size and shape of her kite? explain what happened to the side lengths and angle measures after she made the move. 2. marlon cuts a label in the shape of a capital letter v. he turns the label one - quarter turn clockwise to place it on a package. which way is the open part of the v facing after the rotation? 3. rachel tells jonah that she can turn a square, but he won’t be able to tell that it was turned after she is finished. how can she do this?

Explanation:

Step1: Analyze Darby's kite - translation

Darby slid the kite higher. This is a translation. In a translation, the size and shape of the figure do not change. The side - lengths and angle measures remain the same because translations are rigid motions that preserve distance and angle measures.

Step2: Analyze Marlon's label - rotation

Marlon turns the label (in the shape of a V) one - quarter turn clockwise. A quarter - turn is 90 degrees clockwise. If we assume the V was initially facing upwards, after a 90 - degree clockwise rotation, the open part of the V will face to the right.

Step3: Analyze Rachel's square - rotation

A square has rotational symmetry of order 4. This means that a rotation of 90 degrees, 180 degrees, or 270 degrees will result in a figure that looks the same as the original in some respects. If Rachel turns the square by 90 degrees, 180 degrees, or 270 degrees, the square will still look like a square in the same position (due to its symmetry). For example, a 90 - degree rotation of a square will map it onto itself if we consider the overall shape and position in a plane.

Answer:

1. The size and shape of Darby's kite did not change. The side lengths and angle measures remained the same because translations are rigid motions that preserve distance and angle measures.
2. The open part of the V is facing to the right after a one - quarter (90 - degree) clockwise rotation.
3. Rachel can turn the square by 90 degrees, 180 degrees, or 270 degrees because a square has rotational symmetry of order 4 and will look the same in the same position after these rotations.