Symmetry and Sequences of Transformations

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Translation P maps the point (3, 5) to (1, 7). Which of the following rules defines the translation P?

• P: (x, y) → (3x, 3y)

• P: (x, y) → (x + 2, y -2)

• P: (x, y) → (⅓x, ⅓y)

• P: (x, y) →(x - 2, y + 2)

Answer explanation

Translation is only moving left/right or up down. How far horizontally did you move, and how far vertically did you move?

Two transformations were performed:

1st Transformation: (x, y) → (x - 2, y + 3)

2nd Transformation: (x - 2, y + 3)→(2 - x, y + 3)

What transformations were used?

• a reflection over the x-axis, then a translation

• a reflection over the y-axis, then a translation

• a translation, then a reflection over the x-axis

• a translation then a reflection over the y-axis

Answer explanation

the first transformation must be a translation because we are adding to or subtracting form the original position. When you reflect over the x-axis, the y values negate, when you reflect over the y-axis the x values negate.

Triangle ABC has the coordinates A(2, 7), B( -3, 5), C(3, 2).It is translated in such a way that (x, y) → (-x, -y). What are the coordinates of C'

• (-3, -2)

• (-2, -3

• (-3, 2)

• (3, -2)

Point F translated 4 units right and 6 units down. Which composition would move Point F to the same position?

• translate 4 units left and 2 units down, then 8 units right and 4 units down

• translate 2 units left and 6 units down, then 6 units right and 1 unit down

• translate 5 units right and 4 units down, then 1 unit right and 2 units down

• translate 4 units right and 6 units down, then 4 unis left and 6 units up

Answer explanation

Remember to combine the movements left/right, and combine the movements up/down. The totals for each should equal the distance traveled

Figure A translated to B, then again to C. What is the composition of transformation?

• T<3,5> ∘ T<-5, -1> → T<-2, 4>

• T<-2,4> ∘ T<5, 1> → T<-3,5>

• T<5,3> ∘ T<-1,-5> → T<4,-2>

• T<1,1> ∘ T<-1,3> → T<4,4>

Answer explanation

You can either add the x's and y's, or just look at the image and determine the direct translation

The figure is reflected over the x-axis. Which transformation would produce the same result as this reflection?

• A 90 degree clockwise rotation about the origin and a reflection over the line x = 6

• A 90 degree clockwise rotation about the origin and a reflection over the line y = -4

• A reflection over the line x = 6 and a translation down 8

• A reflection over the line y = 4 and a translation down 8

Answer explanation

Understand what a rotation does to orientation.

Triangle A is rotated 90° counterclockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Which equation represents a line of symmetry for this figure?

• x = -3y

• y = -3x

• x = -3

• y = -3

A regular nonagon (9-sides) has rotational symmetry. What is them minimum number of degrees a regular nonagon must be rotated about its center in order to prove this?

• 360°

• 90°

• 40°

• 30°

Answer explanation

Divide 360° by the number of sides to determine the minim angle of rotation.