1. What transformation is required to change one triangle into the other?
A. Translation
B. Reflection
C. Dilation
D. Rotation
2. Describe the transformation you can use to map vertices of garden RST to corresponding vertices of garden DEF. What does this confirm about the gardens?
A. A dilation with a scale factor of 2. The gardens are not similar.
B. A dilation with a scale factor of 1/2. The gardens are similar.
C. A dilation with a scale factor of 2. The gardens are similar.
D. A dilation with a scale factor of 1/2. The gardens are not similar.
3. Determine whether the two figures are similar using similarity transformations. Explain.
A. △JKL can be mapped onto △MNP by a dilation, so △JKL and △MNP are similar.
B. △JKL can be mapped onto △MNP by a translation, so △JKL and △MNP are similar.
C. There is no similarity transformation that maps △JKL onto △MNP, so △JKL and △MNP are not similar.
D. △JKL can be mapped onto △MNP by a translation followed by a dilation, so △JKL and △MNP are similar.
4. Find a sequence of similarity transformations that maps △JKL to △PQR.
A. You can map △JKL to △PQR with a reflection across the x-axis, followed by a dilation, followed by a 90° clockwise rotation about the origin.
B. You can map △JKL to △PQR with a reflection across the y-axis, followed by a dilation, followed by a 90° clockwise rotation about the origin.
C. You can map △JKL to △PQR with a reflection across the y-axis, followed by a dilation, followed by a 90° counterclockwise rotation about the origin.
D. You can map △JKL to △PQR with a reflection across the x-axis, followed by a dilation, followed by a 90° counterclockwise rotation about the origin.
5.
Determine if the two figures are similar using similarity transformations. Explain.
A. EFGH can be mapped onto ABCD with a dilation of 3 centered at the origin, so the figures are similar.
B. There is no similarity transformation that maps EFGH onto ABCD, so the figures are not similar.
C. EFGH can be mapped onto ABCD with a rotation, so the figures are similar.
D. EFGH can be mapped onto ABCD with a dilation of 4 centered at the origin, so the figures are similar.
1. D. Rotation
2. A. A dilation with a scale factor of 2. The gardens are not similar.
3. C. There is no similarity transformation that maps △JKL onto △MNP, so △JKL and △MNP are not similar.
4. A. You can map △JKL to △PQR with a reflection across the x-axis, followed by a dilation, followed by a 90° clockwise rotation about the origin.
5. B. There is no similarity transformation that maps EFGH onto ABCD, so the figures are not similar.