Free Printable Chapter 3: Rigid Transformations and Symmetry

Worksheets

Chapter 3: Rigid Transformations and Symmetry

Total questions: 20

Worksheet time: 10mins

Name

Class

Date

The support crew for a marathon is setting up a table to give the runners water. They need to set up somewhere along the opposite wall between streets A and B. Determine which point along the wall would allow the runners coming out of street A to run the minimum distance to the water table and then turn down street B.

Point G

Ponit F

Point D

Point E

Quadrilateral WXYZ has vertices W(-3, 5), X(3, 3), Y(-1, 2), and Z(-2, -2). Determine the correct graph and its image in the line y = x.

What is the reflected image of A about line m?

Quadrilateral ABCD with vertices A(–3, 2), B(–1, 4), C(2, 2), and D(1, –2) is reflected in the line y = –2. Which of the following points is a vertex of the image?

A'(-1, 2)

B'(-1, -4)

C'(-2, 6)

D'(1, -2)

Determine which of the transformations is the correct translation of the figure J along the given vector, T.

The graph shows repeated translations that result in the animation of the soccer ball. If you follow the pattern, what will be the coordinates of the translation to position 4?

(5, −3)

(4, −3)

(4, −2)

(5, −2)

$This\ is\ the\ graph\ of\ y=x^2.\ Choose\ the\ correct\ graph\ of\ the\ function\ translated\ along\ the\ vector\ \left(-3,\ 2\right).$

The placement of a green floor tile among white floor tiles is determined using a translation as shown at the right. Describe the translation from tile 1 to tile 2 using coordinate notation and words. Describe the translation from tile 1 to tile 3 using a translation vector.

coordinate notation: (x, y) -> (x + 2, y + 3)

words: The tile is translated 2 tiles right and 3 tiles up. translation vector for tile 1 to tile 3: ⟨4,6⟩

coordinate notation: (x, y) -> (x - 2, y - 3)

words: The tile is translated 2 tiles left and 3 tiles down.

translation vector for tile 1 to tile 3: ⟨2,3⟩

coordinate notation: (x, y) -> (x - 2, y - 3)

words: The tile is translated 2 tiles right and 3 tiles up.

translation vector for tile 1 to tile 3: ⟨2,3⟩

coordinate notation: (x, y) -> (x + 2, y + 3)

words: The tile is translated 2 tiles left and 3 tiles down.

translation vector for tile 1 to tile 3: ⟨4,6⟩

Determine which image is the correct transformation of a rotation of triangle GHI 90° clockwise about point J.

10.

Determine which image is the correct transformation of a rotation of circle T 135° clockwise about point Q.

11.

Determine which image is the correct transformation of a rotation of 180° clockwise about point R.

12.

Triangle EFG is shown here. What is the image of point F after a rotation 270° counterclockwise about the origin?

(−1, 4)

(4, −1)

(−4, −1)

(4, 1)

13.

Triangle MNO has vertices M(-3, 4), N(-4, 1), and O(-1, 2). Choose the graph that correctly displays a translation along <4, 0>and a reflection in the x-axis.

14.

Triangle RST has vertices R(3, 0), S(1, -3), and T(5, -1). Choose the graph that correctly displays a reflection in the y-axis and a translation along <0, 5>.

15.

Triangle RST has vertices R(-3, 0), S(-1, -2), and T(-5, -1). Choose the graph that correctly displays a reflection in the y-axis and a rotation 90° counterclockwise about the origin.