Practicing Point by Point Transformations

ID: popoj-nukul
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Practicing Point by Point Transformations

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Problem 1

1) The figures are congruent. Select all the sequences of transformations that would take Figure 1 to Figure 2. Write each corresponding letter in the answer box and separate letters with commas.

a) Translate by directed line segment ADAD. \quad\quad b) Rotate 180 degrees around point EE.

c) Translate by directed line segment AEAE and reflect across ACAC.

d) Translate by directed line segment CECE and rotate 90 degrees counterclockwise around point EE.

e) Rotate 180 degrees around point CC, translate by directed line segment CECE, and reflect across segment EFEF.

f) Reflect across segment ABAB, rotate clockwise by angle BFEBFE using center FF, then reflect across segment EFEF.

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Problem 2

2) Draw the image of figure ACTSACTS after a clockwise rotation around point TT using angle CTSCTS and then a translation by directed line segment CTCT.

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3) Describe another sequence of transformations that will result in the same image.

Problem 3

4) Draw the image of triangle ABCABC after this sequence of rigid transformations.

1) Reflect across line segment ABAB.

2) Translate by directed line segment uu.

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Problem 4

5) Describe a transformation that takes any point AA to any point BB.

Problem 5

6) Triangle ABCABC is congruent to triangle ABCA'B'C'. Describe a sequence of rigid motions that takes AA to AA' , BB to BB', and CC to CC'.

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Problem 6

7) A quadrilateral has rotation symmetry that can take any of its vertices to any of its other vertices. Select all conclusions that we can reach from this. Write each corresponding letter in the answer box and separate letters with commas.

a) All sides of the quadrilateral have the same length. \quad\quad b) All angles of the quadrilateral have the same measure.

c) All rotations take one half of the quadrilateral to the other half of the quadrilateral.

Problem 7

8) A quadrilateral has a line of symmetry. Select all conclusions that must be true. Write each corresponding letter in the answer box and separate letters with commas.

a) All sides of the quadrilateral have the same length. \quad\quad b) All angles of the quadrilateral have the same measure.

c) Two sides of the quadrilateral have the same length. \quad\quadd) Two angles of the quadrilateral have the same measure.

e) No sides of the quadrilateral have the same length. \quad\quad f) No angles of the quadrilateral have the same measure.

Problem 8

9) Which segment is the image of FGFG when rotated 9090^{\circ} clockwise around point PP?

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Problem 9

10) Which statement is true about a translation?

a) A translation rotates a line.\text{A translation rotates a line.}b) A translation takes a line to a parallel line or itself. \text{A translation takes a line to a parallel line or itself. }c) A translation takes a line to a perpendicular line. \text{A translation takes a line to a perpendicular line. }d) A translation dilates a line.\text{A translation dilates a line.}