Properties of Transformation 1

. A sequence of transformations maps rectangle ABCD onto rectangle A"B"C"D", as shown in the diagram below. Which sequence of transformations maps ABCD onto A'B'C'D' and then maps A'B'C'D' onto A"B"C"D"?

• 1) a reflection followed by a rotation

   

• 2) a reflection followed by a translation

• 3) a translation followed by a rotation

• 4) a translation followed by a reflection

In the diagram below, congruent figures 1, 2, and 3 are drawn. Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?

• 1) a reflection followed by a translation

• 2) a rotation followed by a translation

• 3) a translation followed by a reflection

• 4) a translation followed by a rotation

What is the image of point A (4, 2) after the composition of transformations defined by R 90 o r y = x ?

• (-4, 2)

• (4, -2)

• (-4, -2)

• (2, -4)

5. On the set of axes below, ABC has vertices at A(−2,0), B(2,−4), C(4,2), and DEF has vertices at D(4,0), E(−4,8), F(−8,−4). Which sequence of transformations will map ABC onto DEF?

• 1) a dilation of ABC by a scale factor of 2 centered at point A

• 2) a dilation of ABC by a scale factor of 1/2 centered at point A

• 3) a dilation of ABC by a scale factor of 2 centered at the origin, followed by a rotation of 180° about the origin

• 4) a dilation of ABC by a scale factor of 1 2 centered at the origin, followed by a rotation of 180° about the origin

On the set of axes below, triangle ABC is graphed. Triangles A'B'C' and A"B"C", the images of triangle ABC, are graphed after a sequence of rigid motions. Identify which sequence of rigid motions maps ABC onto A'B'C' and then maps A'B'C' onto A"B"C".

• 1) a rotation followed by another rotation

• 2) a translation followed by a reflection

• 3) a reflection followed by a translation

• 4) a reflection followed by a rotation

Triangles ABC and RST are graphed on the set of axes below. Which sequence of rigid motions will prove ABC ≅ RST?

• 1) a line reflection over y = x

• 2) a rotation of 180° centered at (1,0)

• 3) a line reflection over the x-axis followed by a translation of 6 units right

• 4) a line reflection over the x-axis followed by a

  line reflection over y = x

As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. Under this transformation, which property is not preserved?

• 1) area

• 2) distance

• 3) orientation

• 4) angle measure

. In the diagram below, line m is parallel to line n. Figure 2 is the image of Figure 1 after a reflection over line m. Figure 3 is the image of Figure 2 after a reflection over line n. Which single transformation would carry Figure 1 onto Figure 3?

 

• 1) a dilation

• 2) a rotation

• 3) a reflection

• 4) a translation

Under which transformation would A'B'C', the image of ABC, not be congruent to ABC?

• 1) reflection over the y-axis

• 2) rotation of 90° clockwise about the origin

• 3) translation of 3 units right and 2 units down

• 4) dilation with a scale factor of 2 centered at the origin

The image of DEF is D' E'F'. Under which transformation will he triangles not be congruent?

• 1) a reflection through the origin

• 2) a reflection over the line y = x

• 3) a dilation with a scale factor of 1 centered at (2,3)

• 4) a dilation with a scale factor of 3 2 centered at the origin