Name: _______________________________________ Hour: _______________ Date: __________________

That’s Next Level!

The goal of the game is to get the flag in the bottom left corner to land on top of the other flag and
then progress to the next level. The flag can be shifted to the next square right, left, up or down.
The flag can also be rotated in 90˚ increments counterclockwise or flip across horizontal or vertical
lines. Reflecting and rotating does not change the square that the flag is in.

1. Describe a sequence of moves that would let you pass this level.

2. Now come up with a different sequence of moves. How many sequences are possible?

3. Is there a most efficient sequence to pass this level? Explain.

4. Pedro argues that this level requires a vertical flip, but Jane says it requires a horizontal flip
instead. Who is correct? Give a reason.

5. On your new grid, create a level that requires at least 7 moves. Then have your partner solve it.

SOLVE NEXT IXL:

UYL
Name: _______________________________________ Hour: _______________ Date: __________________

Lesson 3.1 – Introduction to Transformations

QuickNotes

Check Your Understanding

#### and then rotated 90˚ counterclockwise around
1. Right triangle ABC is reflected over !"
point B. Draw triangle ABC after these transformations.

2. The preimage and image of an emoji are shown below. Daija claims that this is a 90˚
counterclockwise rotation. Do you agree or disagree? Explain.

3. Describe two different ways that ∆ABC could be transformed into ∆A’B’C’.
Name: _______________________________________ Hour: _______________ Date: __________________

Lost in Translation

Yesterday we used various transformations to get the flag to move to its new location.
Today we’ll get more specific about how to describe these moves.

1. Describe the similarities and differences between the two triangles.

2. a. Graph ∆ABC after moving it left four and up two.

b. Give the ordered pairs of the new triangle.

c. Describe what happened to the measures of the

three angles and three side lengths of the
triangle after moving it.

3. What is the shortest possible way you could explain to someone how get the top
quadrilateral to move to its new position?

SOLVE NEXT IXL:

RUP, XUS, 6XB
Name: _______________________________________ Hour: _______________ Date: __________________

Lesson 3.2 –Translations

QuickNotes

Check Your Understanding

1. Give the coordinates of the image of polygon BREAD after applying the translation rule
(", $) → (" + 7, $ − 5).

2. Write a translation rule that takes ∆ABC to its image ∆A’B’C’ or explain why it cannot be done.
a) b)

3. Quadrilateral FISH has coordinates F(-8,11), I(-7,9), S (0,6), H(-2,-3) and then is translated so
that H’=(3,-7). Find the coordinates of F’, I’ and S’.
Name: _______________________________________ Hour: _______________ Date: __________________

Mirror, Mirror

1. Use the picture below to answer the following questions.

a. How far is point B away from the line?

b. Reflect point B over the line. Label it B’.

c. How far is the new point away from the line?

2. Now we will reflect an entire triangle.

a. Reflect !, #, and % over the y-axis. Then connect the points using a ruler.
b. Write the coordinates of both triangles in
the table below.
J= ( , ) K= ( , ) L= ( , )

J’= ( , ) K’= ( , ) L’= ( , )

c. What patterns do you see in the

coordinates of the preimage and the
image?

d. How do the sizes of the two triangles compare?

3. What happens if we reflect over the x-axis instead?

a. Reflect ∆!#% over the x-axis.

b. Write the coordinates of both triangles in

the table below.
J= ( , ) K= ( , ) L= ( , )

J’= ( , ) K’= ( , ) L’= ( , )

c. What patterns do you see in the

coordinates of the preimage and the
image?
SOLVE NEXT IXL:
KUX, SVY, 74Z
Name: _______________________________________ Hour: _______________ Date: __________________

4. Now let’s reflect over a different kind of line.

a. How is this line different than the ones we worked with before?

b. Will each vertex of the triangle move the same distance in the reflection? How do you
know?

5. Let’s see if you’re right!

a. Place your patty paper on top of the graph and trace ∆ABC, as well as the line we want
to reflect over. Be sure to label which point is A, B, and C.

b. Fold the patty paper directly on the line to reflect the triangle.
c. Take a look at where the triangle landed and write the coordinates of both triangles in
the table below. Then plot ∆A’B’C’ on your graph.

A= ( , ) B= ( , ) C= ( , )
A’= ( , ) B’= ( , ) C’= ( , )

d. What patterns do you notice in the coordinates of the preimage and the image?

6. Which point is closest to the line of reflection: B or B’? Give a convincing argument.
Name: _______________________________________ Hour: _______________ Date: __________________

Lesson 3.3 –Reflections

QuickNotes

Check Your Understanding

1. Draw ∆ABC after a reflection over a) the y-axis and b) the line y=x.
a) b)

2. Give the coordinates of the image of polygon BREAD after reflecting over the x-axis.

3. ∆DEF has coordinates given by D=(2,7), E=(3,4), and F=(-1,-2). When ∆DEF is reflected across
a certain line, E’ stays in the same position, and D’=(4,7). What are the coordinates of F’?
Name: _______________________________________ Hour: _______________ Date: __________________

Spinning Out

We’ve already seen how we can translate and reflect shapes in the coordinate grid. Today we’ll
explore how rotations work. The table shown below will be filled out as you move through the
investigation.

1. Plot the points A(2, 1), B(6, 1), and C(4, 5) on the coordinate grid below. Label each vertex.

A=(2,1) B=(6,1) C=(4,5)

Rotation of 90˚ CCW

Rotation of 180˚ CCW

Rotation of 270˚ CCW

2. Place your patty paper on top of the grid. Trace the triangle and label point A, B, and C.
3. Trace the x-axis in one color and the y-axis in a different color.
4. Turn your patty paper 90˚ counterclockwise.
a. Record the new coordinates of your triangle in the table.
b. What do you notice about the coordinates of the original and the new triangle?

5. Return your patty paper to its original position. Turn your patty paper 180˚
counterclockwise.
a. Record the new coordinates of your triangle in the table.
b. What do you notice about the coordinates of the original and the new triangle?

6. Return your patty paper to its original position. Now turn your patty paper 270˚
counterclockwise.
a. Record the new coordinates of your triangle in the table.
b. What do you notice about the coordinates of the original and the new triangle?

7. A star in the coordinate plane has two of its points at (3,-5) and (-2,-7). After a rotation, the
first point moved to (-5,-3). Where did the other point move? How many degrees was the
star rotated?
SOLVE NEXT IXL:
HHS, AC9, 2F8
Name: _______________________________________ Hour: _______________ Date: __________________

Lesson 3.4 – Rotations

QuickNotes

Check Your Understanding

1. Graph quadrilateral ABCD after a 180˚ rotation

about the origin. Label the new vertices with prime
notation.

2. Give the coordinates of the image of polygon BREAD after a 90˚ counterclockwise
rotation about the origin.

3. Paul, Jess, and Javier were asked to identify the transformation that took place. Paul
said it was a 90˚ CCW rotation. Jess said it was a translation 9 to the right and 1 down.
Javier said it was a 270˚ CCW rotation. Who is correct? Explain.