GEOMETRY ACHAPTER 11ROTATIONS ASSIGNMENT 2

1. What type of transformations are isometries?Reflection, Translation, Rotation, any transformation that preserves distance.

2. If you reflect a figure over two parallel lines, the result is a translation.

3. A figure is translated with a magnitude of 25 cm. This is the same as a reflection over two parallel lines that are how far apart?

If a figure is reflected over two parallel lines, the resulting transformation is a translation. The magnitude of the translation vector is twice the distance between the two lines. If |v| = 25 cm, then the distance between the two lines is 25 2 = 12.5 cm.

4. How many lines of symmetry does each figure have?

One - Vertical

None

4. How many lines of symmetry does each figure have?

Five

5. If you rotate ΔABC 120° clockwise, then rotate ΔA’B’C’ 68° counter clockwise, describe the single rotation of ΔABC to result in ΔA’’B’’C’’.

120 – 68 = 52° clockwise

6. A’B’ is the image of AB rotated about point C.What is the angle of rotation?

AOA’ or BOB’ In what direction?

Counter Clockwise

B’ C’ D’ E’

B’(-2, 1)C’(-8, 1)D’(-8, 10)E’(-2, 10)

B(1, 2)C(1, 8)D(10, 8)E(10, 2)

D’ E’ F’ G’

D(8, 1)E(9, 1)F(9, 10)G(8, 10)

D’(-8, -1)E(-9, -1)F(-9, -10)G(-8, -10)

V’ U’ W’

U(-5, -2)V(-2, -2)W(-6, 8)

U’(0, 5)V’(0, 2)W’(-8, -8)

F’ G’ H’

F(-9, -7)G(-5, -7)H(-5, 1)

F’(-9, -1)G(-5, -1)H(-5, -9)

y = x + 1

A(1, -1)B(2, 1)C(-2, 3)

A’(-2, 2)B’(0, 3)C’(2, -1)

A’ B’ C’

10. Graph ∆ABC with vertices A(1, -1), B(2, 1), and C(-2, 3). Graph the line of reflection y = x + 1. Reflect ∆ABC in y = x + 1. List the vertices of the image.