Map a Figure Onto Itself

Which transformation will map an image onto itself?

• A translation 3 units right and 3 units up

• A rotation 360^o clockwise

• A reflection over the y-axis followed by a translation 3 units down

• A dilation followed by a 90^o clockwise rotation

Answer explanation

A 360 degree rotation is a full rotation, which means. the figure ends up where it started.

The preimage above is rotated 90^o counterclockwise. How do the side lengths in the preimage compare to the side lengths in the image?

• Some of the side lengths increase in measure and other side lengths decrease in measure.

• The measures of the side lengths double.

• The measures of the side lengths decrease by one third.

• The measures of the side lengths are the same.

Answer explanation

A rotation is a rigid transformation, which means size is unchanged when applied. That means the side lengths are the same.

What will be the new position of the given point after rotating 90^o counterclockwise or 270^o clockwise?

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Answer explanation

Counterclockwise follows the numbering scheme of the quadrants. If the preimage is in the bottom left quadrant (QIII), then the new image after a 90 degree counterclockwise rotation will be in the next quadrant (QIV) in the bottom right.

What is the scale factor that you must use to map FROG to F'R'O'G'?

Answer explanation

FROG is the larger figure and the preimage. F'R'O'G' is the smaller figure and the new image. This means the figure was dilated by a value less than 1 in order to get smaller.

The side lengths on F'R'O'G' are all half as long as those of FROG. This means FROG must have been dilated by

$\frac{1}{2}$ (or 0.5)

• 90^o CW rotation around the origin

• Reflect across x-axis

• Translate 8 units up

Which of the following transformations will carry figure onto itself? Hint: make up a random point (where x and y are different--not 1,1 or 2, -2) an try each transformation OR DRAW A PICTURE.

• A reflection across the line y=x and then a rotation of 90 degrees clockwise.

• A rotation of 450 degrees clockwise and then, a rotation of 90 degrees counterclockwise.

• A reflection across the y-axis and then, a reflection across the x-axis.

• A translation 5 units down, 3 units right and then, a rotation of 180 degrees clockwise.

Which transformation maps the parallelogram onto itself?

• a reflection across line x = 2

• a reflections across line y = 2

• a $180\degree\$ clockwise rotation around (2,2)

The figure below shows two perpendicular lines 𝑗 and 𝑘 intersecting at point 𝐷 in the interior of a rectangle. Line 𝑗 bisects both the top and bottom sides of the rectangle. Line 𝑘 bisects both the left and right sides of the rectangle. Which transformation will always carry the figure onto itself?

Select All that apply.

• a reflection across line 𝑗.

• A reflection across line 𝑘.

• A rotation of 90° clockwise about point 𝐷.

• A rotation of 180° clockwise about point 𝐷.

• A rotation of 270° clockwise about point 𝐷.

Which transformation will map the right triangle onto itself?

• 90 degree rotation

• 180 degree rotation

• 270 degree rotation

• none of the above choices

Describe the rotational symmetry for a regular pentagon.

• A regular pentagon has a central angle of 72° and will map onto itself after rotations of 72°, 144°, 216°, and 288°.

• A regular pentagon has five axes of symmetry.

• A regular pentagon has four-fold rotational symmetry.

• A regular pentagon has a central angle of 45° and will map onto itself after rotations of 45°, 90°, 135°, 180°, 225°, 270°, and 325°.