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Question
What transformations figures 1 and 2 require to form figure 3?
What transformations figures 1 and 2 require to form figure 3?
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Solution
The correct option is D Figure 1: Rotation 90o counterclockwise about the origin, translation;
Figure 2: Dilation about the origin with a scale factor of 0.5, reflection on the y-axis, translation
Let’s observe both the preimage and the image and go through the options one-by-one.
Here, in option A, we notice that figure 2 undergoes dilation about the origin with a scale factor of 2. This means rectangle E′F′G′H′ is twice the size of rectangle EFGH, which is not the desired image. Hence, option A is the incorrect option.
In option B, figure 1 undergoes rotation of 90° counterclockwise about the origin. This means the image A′B′C′D′ lies in the second quadrant, which is the desired image. Similarly, figure 2 undergoes dilation about the origin with a scale factor of 0.5. This means rectangle E′F′G′H′ is half the size of rectangle EFGH, which is also the desired image. Hence, option B may be the correct option.
In option C, figure 1 undergoes rotation of 180o counterclockwise about the origin. This means the rectangle A′B′C′D′ lies in the third quadrant, which is not the desired image. Hence, option C is the incorrect option.
In option D, figure 1 undergoes rotation of 90o clockwise about the origin. This means the rectangle A′B′C′D′ lies in the fourth quadrant, which is not the desired image. Hence, option D is the incorrect option.
Step 1:
Figure 1: Rotation 90o counterclockwise about the origin
Step 2:
Figure 1: Translation of 1 unit toward the left and then 2 units top
Step 3:
Figure 2: Dilation about the origin with a scale factor of 0.5
Step 4:
Figure 2: Reflection on the y-axis
Step 5: Translation of 2 units toward the left and then of 1 unit up
Hence, the correct answer is option B.
Figure 2: Dilation about the origin with a scale factor of 0.5, reflection on the y-axis, translation
Let’s observe both the preimage and the image and go through the options one-by-one.
Here, in option A, we notice that figure 2 undergoes dilation about the origin with a scale factor of 2. This means rectangle E′F′G′H′ is twice the size of rectangle EFGH, which is not the desired image. Hence, option A is the incorrect option.
In option B, figure 1 undergoes rotation of 90° counterclockwise about the origin. This means the image A′B′C′D′ lies in the second quadrant, which is the desired image. Similarly, figure 2 undergoes dilation about the origin with a scale factor of 0.5. This means rectangle E′F′G′H′ is half the size of rectangle EFGH, which is also the desired image. Hence, option B may be the correct option.
In option C, figure 1 undergoes rotation of 180o counterclockwise about the origin. This means the rectangle A′B′C′D′ lies in the third quadrant, which is not the desired image. Hence, option C is the incorrect option.
In option D, figure 1 undergoes rotation of 90o clockwise about the origin. This means the rectangle A′B′C′D′ lies in the fourth quadrant, which is not the desired image. Hence, option D is the incorrect option.
Step 1:
Figure 1: Rotation 90o counterclockwise about the origin
Step 2:
Figure 1: Translation of 1 unit toward the left and then 2 units top
Step 3:
Figure 2: Dilation about the origin with a scale factor of 0.5
Step 4:
Figure 2: Reflection on the y-axis
Step 5: Translation of 2 units toward the left and then of 1 unit upHence, the correct answer is option B.Suggest Corrections
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