Multiple Rigid Transformations

Which sequence of transformations is used to transform the original image to the final image? Original: ABCD Final: A" B" C"D"

• Reflect over the x-axis and then rotate clockwise 90 around the origin.

• Rotate counterclockwise 90 around the origin and then translate 8 units left.

• Reflect over the y-axis and then rotate counterclockwise 90 around the origin.

• Rotate clockwise 90 around the origin and then translate 8 units left.

Henry starts with the two parallel line segments shown. She correctly reflects the segments across the x-axis and then translates them following the rule (x,y) --> (x-2,y+5). Which statements about the reflection and translation of the line segments are true? Select all that apply

• The final image will result in parallel segments slanted in the opposite direction and the same distance apart as the preimage segments.

• The coordinates of point C’ in the final image are (1,4).

• When reflected over the x-axis, the coordinates of point A become (2,–4).

• The final image will result in perpendicular segments that intersect at point (0,1).

• The final image will result in parallel segments slanted in the same direction and closer together than the preimage segments.

Quadrilateral QRST is rotated 360 counterclockwise around a center at one of its vertices. Which statements must be true? Select all that apply.

• Q'R'S'T' appears as a translation of QRST .

• Q'R'S'T' appears as a reflection of QRST .

• The coordinate x- and y-values of Q'R'S'T' are the same as QRST coordinate x- and y-values

• Image Q'R'S'T' is mapped exactly on top of QRST .

• The coordinate x- and y-values of Q'R'S'T' are the reverse of QRST coordinate x- and y-values

Which transformations could be used to transform from the original image to the final image?

• Translate 7 units up.

• Translate 8 units right.

• Rotate 90 counterclockwise around the origin

• Rotate 180 around the origin.

• Translate 5 units down.

Point (4,5) is rotated 180. What are the new coordinates?

• (-4,-5)

• (-5,4)

• (4,-5)

Point (4,5) is rotated 90 clockwise. What are the new coordinates?

• (-4,-5)

• (-5,4)

• (5,-4)

Point (4,5) is rotated 90 counter-clockwise. What are the new coordinates?

• (-4,-5)

• (-5,4)

• (4,-5)

Ronnie performed a series of rigid transformations on Figure 1. The result of the transformations is Figure 2 as shown on the coordinate grid. What is the sequence of transformations that Ronnie followed so that Figure 1 lies exactly on top of Figure 2?

• a reflection across the x-axis and then a translation of 6 units to the right and 3 units up.

• a 90 counterclockwise rotation about the origin and then a translation of 5 units left and 3 units down

• a reflection across the y-axis and then a translation of 5 units to the left and 5 units down

• a 270 counter-clockwise rotation about the origin and then a reflection across the x-axis

If you perform any sequence of rigid transformations, what must always be true?

• The figures will be congruent.

• The figures will be different sizes.

Which of the following transformations is NOT an isometry?

• Reflections

• Rotations

• Translations

• Dilations