Students can use the Spectrum Math Grade 8 Answer Key Chapter 5 Lesson 5.4 Transformation Sequences as a quick guide to resolve any of their doubts.
Spectrum Math Grade 8 Chapter 5 Lesson 5.4 Transformation Sequences Answers Key
If there exists a sequence of translations, reflections, rotations, and/or dilations that will transform one figure into the other, the two figures are either similar or congruent. Similar figures are the same shape but not the same size while congruent shapes are both the same shape and the same size. Follow the sequence of transformations to determine if two figures are similar or congruent.
Determine if a set of transformations exist between figures 1 and 2. Then, write similar, congruent, or neither.
Question 1.
a.
Answer: congruent
If there exists a sequence of translations, reflections, rotations, and/or dilations that will transform one figure into the other, the two figures are either similar or congruent. Similar figures are the same shape but not the same size while congruent shapes are both the same shape and the same size.
b.
Answer: Neither
If there exists a sequence of translations, reflections, rotations, and/or dilations that will transform one figure into the other, the two figures are either similar or congruent. Similar figures are the same shape but not the same size while congruent shapes are both the same shape and the same size.
c.
Answer: Neither
If there exists a sequence of translations, reflections, rotations, and/or dilations that will transform one figure into the other, the two figures are either similar or congruent. Similar figures are the same shape but not the same size while congruent shapes are both the same shape and the same size.
Question 2.
a.
Answer: neither
If there exists a sequence of translations, reflections, rotations, and/or dilations that will transform one figure into the other, the two figures are either similar or congruent. Similar figures are the same shape but not the same size while congruent shapes are both the same shape and the same size.
b.
Answer: congruent
If there exists a sequence of translations, reflections, rotations, and/or dilations that will transform one figure into the other, the two figures are either similar or congruent. Similar figures are the same shape but not the same size while congruent shapes are both the same shape and the same size.
c.
Answer: Similar
If there exists a sequence of translations, reflections, rotations, and/or dilations that will transform one figure into the other, the two figures are either similar or congruent. Similar figures are the same shape but not the same size while congruent shapes are both the same shape and the same size.
Sometimes the order of the steps in a transformation sequence will vary, but every shape has a specific sequence it must go through in order to be transformed.
Step 1: The figure is reflected across the y-axis.
Step 2: The figure is rotated 90°.
Step 3: The figure is translated by -8 along the y-axis.
Step 4: The figure is decreased by 20% (dilation in reverse).
Write the steps each figure must go through to be transformed from figure 1 to figure 2.
Question 1.
a.
Step 1 : _____
Step 2 : _____
Step 3 : _____
Answer:
Step 1: The figure is rotated 90°.
Step 2: The figure is dilated by 2.
Step 3: The figure is translated by +9 along the y-axis and -10 on x-axis.
b.
Step 1 : _____
Step 2 : _____
Step 3 : _____
Answer:
Step 1: The figure is reflected on the x-axis.
Step 2: The figure is translated by 6 along the y-axis.
Question 2.
a.
Step 1 : _____
Step 2 : _____
Step 3 : _____
Answer:
Step 1: The figure is rotated 90°.
Step 2: The figure is dilated by 2.
Step 3: The figure is translated by -12 along the y-axis.
b.
Step 1 : _____
Step 2 : _____
Step 3 : _____
Answer:
Step 1: The figure is reflected on the x-axis.
Step 2: The figure is rotated 90°.
Step 3: The figure is dilated by 2.