Mid-Unit Assessment

1.

Which sequence of transformations would not return a shape to its original position?

A.

Translate 3 units up, then 3 units down

B.

Reflect over line $p$ , then reflect over line $p$ again

C.

Translate 1 unit to the right, then 4 units to the left, then 3 units to the right

D.

Rotate $120^\circ$ counterclockwise around center $C$ , then rotate $220^\circ$ counterclockwise around $C$

Answer:

Rotate $120^\circ$ counterclockwise around center $C$ , then rotate $220^\circ$ counterclockwise around $C$

Teaching Notes

Students who select choice A or choice C may struggle to understand a sequence of translations. Students who select choice B may have trouble visualizing a reflection over a line which is not drawn for them. Students who do not select choice D may incorrectly add the angle measures of the rotation or not consider the direction of the rotations.

2.

Select all the pairs where Figure $K$ is the image of Figure $J$ after a reflection, rotation, or translation.

A.

Pair A

B.

Pair B

C.

Pair C

D.

Pair D

E.

Pair E

F.

Pair F

Answer: B, D, F

Teaching Notes

Students who select choice A may notice that a rotation takes some of the sides of

J

to

K

. Students who select choice B may notice that a translation will take 3 of the sides of

J

to

K

. Students who select choice E may notice that a reflection across

\ell

will take 7 of the sides of

J

to

K

.

3.

Line segment $A’B’$ is the image of $AB$ after a $180^\circ$ rotation around point $P$ .

Select all of the true statements about the figure.

A.

AB

is the same length as

A’B’

.

B.

AB

is parallel to

A’B’

.

C.

AB

is the same length as

BB’

.

D.

Angle

ABP

is the same measure as angle

A’B’P

.

E.

Angle

ABP

and angle

A’B’P

are vertical angles.

Answer: A, B, D

Teaching Notes

Students who select choice C identify parts of the figure that are not corresponding parts as having the same length. Students who select choice E may identify that the angles are the same measure but do not recall that vertical angles share a vertex.

4.

Here are three pairs of figures:

Which transformation takes Figure A to Figure B in Pair 1:
a translation, rotation, or reflection?
Which transformation takes Figure A to Figure B in Pair 2:
a translation, rotation, or reflection?
Which transformation takes Figure A to Figure B in Pair 3:
a translation, rotation, or reflection?

Answer:

Rotation
Reflection
Translation

Teaching Notes

Students are presented with a shape and an image that is a translation, rotation, or reflection of the given shape. Students then identify the translation, rotation, or reflection. For this task, the shapes are on a grid.

5.

Explain why Figure B is not the image of Figure A after a rotation using center $P$ .
Explain why Figure B is not the image of Figure A after a rreflection using line $\ell$ .

Answer:

The shortest side of Figure A is longer than the shortest side of Figure B. Since rotations do not change lengths, Figure B is not a rotation of Figure A.
The angles in Figure B do not match the corresponding angles in Figure A. Some of the angles in Figure A look like right angles while some corresponding angles in Figure B are definitely not right angles.

Minimal Tier 1 response:

Work is complete and correct.
Sample:

The side lengths of the figures aren’t the same.
The angle measures of the figures aren’t the same.

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: Generic statement about shape, such as “The two figures have different shapes”; stating that the second shape has different side lengths without being specific (only one of the side lengths is visibly different); stating that the first shape has different angle measures without being specific.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: Omitted explanations; stating that Figure B is the image of Figure A.

Teaching Notes

Segment lengths and angle measures are preserved by translations, reflections, and rotations. If two shapes do not have the same side lengths or angles, then one of them cannot be obtained from the other by a rigid transformation.

6.

Point $A$ is located at coordinates $(\text{-}4,3)$ .

What are the coordinates of each point?

Point $B$ is the image of $A$ after a rotation of $180^\circ$ using $(0,0)$ as center.
Point $C$ is the image of $A$ after a translation 2 units to the right, then a reflection using the $x$ -axis.
Point $D$ is the image of $A$ after a reflection using the $y$ -axis, then a translation 2 units to the right.

Answer:

Point $B: (4, \text{-}3)$
Point $C: (\text{-}2, \text{-}3)$
Point $D: (6, 3)$

Teaching Notes

In order to apply rigid transformations to polygons and other shapes, students practice applying them to single points. Lines of reflection are restricted to the $x$ - and $y$ -axes, while rotations are about the origin and are multiples of $90^\circ$ .

7.

Draw the image of this figure under a $90^\circ$ clockwise rotation using center $P$ .
<p>A quadrilateral on a grid. The figure has a vertex at 1 unit right and 4 units up. Another vertex at 1 unit right and 7 units up. Another vertex at 3 units right and 5 units up. Another vertex 2 units right and 7 units up. A point, labeled P, is 4 units to the right, 4 units up.</p>
The figure on the left is reflected using line $\ell$ to form the image on the right. Use the information in the original figure to label the corresponding side lengths and angle measures of the image.
<p>Two quadrilaterals on a grid. A figure has a vertex at 1 unit right and 1 unit up. The interior angle at this vertex is labeled 63 degrees. Another vertex is at 3 units right and 1 unit up. The interior angle at this vertex is labeled 108 degrees. Another vertex is at 4 units right 4 units up. The length between these two vertices is labeled 3 point 2. Another vertex is at 2 units right and 3 units up. The interior angle at this vertex is labeled as 143 degrees. The length between these two vertices is labeled as 2 point 2. A vertical line labeled l appears 6 units to the right on the grid. Another figure has a vertex at 9 units to the right, 1 unit up. Another vertex at 8 units to the right and 4 units up. Another vertex at 10 units to the right, 3 units up. Another vertex at 11 units to the right and 1 unit up.</p>

Answer:

Minimal Tier 1 response:

Work is complete and correct, with complete explanation or justification.
Sample:

See diagram. The image is drawn correctly, with all vertices in correct locations, and all edges drawn.
See diagram

Tier 2 response:

Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification.
Sample errors: One point in the image for part a is incorrectly located; the image in part a is drawn with a $90^\circ$ counterclockwise rotation; one angle or length in part b is incorrect.

Tier 3 response:

Work shows a developing but incomplete conceptual understanding, with significant errors.
Sample errors: More than one point in part a is incorrectly located; the image in part a is drawn with a $180^\circ$ rotation or other incorrect angle of rotation; more than one angle or length in part b is incorrect (this includes the case where all angles and lengths have been drawn in as if the image were a rotation or if it were the original shape without reflection).

Tier 4 response:

Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.
Sample errors: major errors or omissions in one problem part along with errors in the other; two or more error types from Tier 3 response

Teaching Notes

A figure is given on a grid. Students apply a rigid transformation to the shape, drawing the final result. Students also identify and label corresponding parts in an image given information on the original figure.