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5.4 Sequence of Transformations (Due 1/29/25)

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Last updated about 9 hours ago
12 questions
Required
30
Required
30
Required
30
Required
40
Required
10
Essential Question: How do different transformations, when applied in sequence, affect the shape, size, and position of a geometric figure?

Learning Target: Students will be able to apply a sequence of transformations, including translations, rotations, and reflections, to a geometric figure and describe their combined effect on its position and orientation.

Complete the entire document and use full sentences when prompted for full credit.

Responses without work will receive no points.

Sequence of Transformations

Required
5
Question 1a
1a.

Use this pre-image to show a reflection over the y-axis.

Required
5
Question 1b
1b.

Use this pre-image to show a 90 degree rotation counter-clockwise with respect to origin.

Required
10
Question 2
2.
Start with Triangle ABC with vertices A(-3, 7), B(-2, 1), and C(-5, 2):

Perform the following sequence of transformations. Graph and label each new image:

a) reflection in the x-axis
A'_______
B'_______
C'_______
b) translation along the rule (x, y) → (x + 9, y + 2)
A''_______
B''_______
C''_______
Question 3
3.
Start with Triangle ABC with vertices A(-3, 7), B(-2, 1), and C(-5, 2):

Perform the following sequence of transformations. Graph and label each new image:

a) rotate 270° counterclockwise about the origin
A'_______
B'_______
C'_______

b) reflect on the line y=x
A''_______
B''_______
C''_______
Question 4
4.
Start with Triangle GHI with vertices G(-1, 6), H(-1, 3), and I(-6, 6):

Perform the following sequence of transformations. Graph and label each new image:

a) translation along the vector <-2, -5>
G'_______
H'_______
I'_______

b) reflection in the line y-axis
G''_______
H''_______
I''_______
Question 5
5.
Start with Rhombus PQRS with vertices P(-1, -3), Q(3, -4), R(4, -8), and S(0, -7):

Perform the following sequence of transformations. Graph and label each new image:

a) translation along the vector <4,10>
P'_______
Q'_______
R'_______
S'_______
b) 90° counterclockwise rotation about the origin
P''_______
Q''_______
R''_______
S''_______
Required
5
Question 6a
6a.

Required
10
Question 6b
6b.

Required
5
Required
20
Question 7
7.

How does this reflection show that the red triangle and blue triangle are congruent? Is there a way to prove this is true?

Explain using evidence from the graph.

Question 1c
1c.

Use this pre-image to show a) a reflection over the y-axis and b) a 90 degree rotation counter-clockwise with respect to origin.

Question 6c
6c.

Question 6d
6d.