Sequences of Congruence Transformations

. Triangle FGH and triangle F'G'H' are shown on the coordinate grid above.

Which sequence of transformations could be applied to triangle FGH to create triangle F'G'H'?

• a translation 3 units left followed by a translation 1 unit up

• a reflection across the x-axis followed by a rotation 180° clockwise about the origin

• a rotation 180° clockwise about the origin followed by a translation 3 units up and then a translation 1 unit right

• a reflection across the y-axis followed by a rotation 90° counterclockwise about the origin and then a reflection across the x-axis

On the coordinate grid shown below, pentagon J is similar to pentagon K.

Which sequence of transformations could be applied to pentagon J to create pentagon K?

• a reflection across the y-axis, then a translation 4 units right

• a reflection across the x-axis, then a translation 2 units up and 8 units right

• a rotation 90° clockwise about the origin, then a translation 1 unit down and 5 units right

• a rotation 90° counterclockwise about the origin, then a translation 3 units up and 7 units right

Triangle RST and triangle R'S'T' are congruent. Both triangles are graphed on the coordinate grid shown above.

Which sequence of transformations could be used to show the congruence between the triangles?

• a translation 3 units up and then a translation 5 units to the right

• a translation 2 units to the right and then a reflection across the y-axis

• a reflection across the y-axis and then a translation 1 unit to the right and 3 units up

•  a translation 1 unit to the right and 3 units up and then a reflection across the y-axis

Quadrilateral ABCD and quadrilateral A'B'C'D' are shown on the coordinate grid above.

Which sequence of transformations could be used to map quadrilateral ABCD onto quadrilateral A'B'C'D'?

• a reflection across the x-axis, followed by a dilation centered at the origin with a scale factor of 0.5

• a dilation centered at the origin with a scale factor of 0.5, followed by a reflection across the y-axis

• a translation 4 units to the right, followed by a dilation centered at the origin with a scale factor of 0.5

• a rotation of 180° about the point (0, ^–0.5), followed by a dilation centered at the origin with a scale factor of 0.5

Rectangle ABCD becomes rectangle A'B'C'D' under a translation of 2 units to the left and 4 units down.

What are the coordinates of A' ?

• (-2,-4)

• (-4,0)

• (-4,-2)

• (-4,-6)

The Bolt Soda Company is designing a logo. They start with the figure shown in the third quadrant. They then add the rotation of this figure 90º clockwise about the origin to the design. What does the new design look like?

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Pentagon A is congruent to pentagon B. Which series of transformations can be used to verify this congruence?

Use pentagon A as the pre-image.

• rotate 90º clockwise, then reflect over x-axis

• reflect over x-axis, then reflect over y-axis

• rotate 90º clockwise, then translate 4 down

• reflect over x-axis, then translate 4 right

• Reflection over the x-axis and a translation (x, y-2)

• Reflection over the y-axis and a translation of (x, y-2)

• translation of (x +12, y) and a rotation of $90\degree$  clockwise around the origin

Which figure can be transformed into Figure P by a translation of 2 units to the right followed by a reflection across the x-axis?

• Figure J

• Figure K

• Figure L

• Figure M

• Figure J

• Figure M

• Figure N

• Figure P