To translate the quadrilateral ADCB 5 units to the left and 2 units down, you need to adjust the coordinates of each point as follows:
- Translate 5 units to the left: This means you will subtract 5 from the x-coordinate of each point.
- Translate 2 units down: This means you will subtract 2 from the y-coordinate of each point.
If the original coordinates of points A, D, C, and B are given as \( A(x_A, y_A) \), \( D(x_D, y_D) \), \( C(x_C, y_C) \), and \( B(x_B, y_B) \), then the new coordinates after the translation will be:
- \( A'(x_A - 5, y_A - 2) \)
- \( D'(x_D - 5, y_D - 2) \)
- \( C'(x_C - 5, y_C - 2) \)
- \( B'(x_B - 5, y_B - 2) \)
Now, we need to evaluate the possible answers given the translated points.
Let's analyze the possible results:
- A’(-1,-4), D’(-1,1), C’(4,-2), B’(2,-5)
- A’(9,-4), D’(9,1), C’(13,-2), B’(12,-5)
- A’(-1,0), D’(-1,5), C’(4,2), B’(2,-1)
- A’(9,0), D’(9,5), C’(13,2), B’(12,-1)
To determine which coordinate set corresponds to the translation:
- The x-coordinates need to be decreased by 5.
- The y-coordinates need to be decreased by 2.
We don't know the original coordinates A, D, C, and B, so we cannot definitively calculate the new coordinates. However, we can check each option logically based on the changes indicated:
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If the original points were A(4, -2), D(4, 3), C(9, 0), and B(7, -3), this translation results in:
- A'(4 - 5, -2 - 2) = (-1, -4)
- D'(4 - 5, 3 - 2) = (-1, 1)
- C'(9 - 5, 0 - 2) = (4, -2)
- B'(7 - 5, -3 - 2) = (2, -5)
So Option 1 matches this translation.
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Option 2 does not correspond when applying the translation.
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Option 3 does not correspond when applying the translation.
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Option 4 also does not correspond when applying the translation.
Given this evaluation, the correct answer is:
A’(-1,-4), D’(-1,1), C’(4,-2), B’(2,-5).
1 answer