Question

lesson 5 - session 3 describing sequences of transformations involving dilations > for each pair of figures, describe a sequence of three or fewer transformations that can be used to map one figure onto the other.

Explanation:

Step1: Analyze figure - 1

For the first pair of figures (A and B), first, we can perform a rotation of 180 - degrees about the origin. This will change the orientation of figure A to match the general orientation of figure B in terms of the way it is tilted. Then, we can perform a translation to move the rotated figure A to the exact position of figure B.

Step2: Analyze figure - 2

For the second pair of figures (D and C), we first note that there is a size - change. We can perform a dilation with a scale factor of 1/2 to reduce the size of figure D to match the size of figure C. Then, we perform a reflection over the x - axis to flip figure D to the position of figure C.

Step3: Analyze figure - 3

For the third pair of figures (F and G), we can perform a dilation with a scale factor of 1/2 to reduce the size of figure F to match figure G. Then, we can perform a reflection over the y - axis to flip figure F to the position of figure G.

Step4: Analyze figure - 4

For the fourth pair of figures (J and K), we can first perform a dilation to change the size of figure J to match figure K. Then, we can perform a rotation and a translation to map figure J onto figure K.

1. Rotation of 180 - degrees about the origin and then translation.
2. Dilation with scale factor 1/2 and then reflection over the x - axis.
3. Dilation with scale factor 1/2 and then reflection over the y - axis.
4. Dilation, rotation and translation.

Answer:

Step1: Analyze figure - 1

For the first pair of figures (A and B), first, we can perform a rotation of 180 - degrees about the origin. This will change the orientation of figure A to match the general orientation of figure B in terms of the way it is tilted. Then, we can perform a translation to move the rotated figure A to the exact position of figure B.

Step2: Analyze figure - 2

For the second pair of figures (D and C), we first note that there is a size - change. We can perform a dilation with a scale factor of 1/2 to reduce the size of figure D to match the size of figure C. Then, we perform a reflection over the x - axis to flip figure D to the position of figure C.

Step3: Analyze figure - 3

For the third pair of figures (F and G), we can perform a dilation with a scale factor of 1/2 to reduce the size of figure F to match figure G. Then, we can perform a reflection over the y - axis to flip figure F to the position of figure G.

Step4: Analyze figure - 4

For the fourth pair of figures (J and K), we can first perform a dilation to change the size of figure J to match figure K. Then, we can perform a rotation and a translation to map figure J onto figure K.

1. Rotation of 180 - degrees about the origin and then translation.
2. Dilation with scale factor 1/2 and then reflection over the x - axis.
3. Dilation with scale factor 1/2 and then reflection over the y - axis.
4. Dilation, rotation and translation.