To determine the coordinates of shape A'B'C'D' after the given transformations (translating 1 space to the left and reflecting over the y-axis), we need to first understand how to perform each transformation.
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Translation 1 space to the left: To translate a point (x, y) to the left by 1 unit, the new coordinates will be (x - 1, y).
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Reflection over the y-axis: Reflecting a point (x, y) over the y-axis means the x-coordinate changes sign, resulting in (-x, y).
Let's denote the original coordinates of shape A'B'C'D' as (A, B, C, D). We will apply these transformations step by step.
First, let’s denote the original coordinates as:
- A(x_1, y_1)
- B(x_2, y_2)
- C(x_3, y_3)
- D(x_4, y_4)
After we translate 1 space to the left:
- A'(x_1 - 1, y_1)
- B'(x_2 - 1, y_2)
- C'(x_3 - 1, y_3)
- D'(x_4 - 1, y_4)
Now, we reflect these new points over the y-axis:
- A''(- (x_1 - 1), y_1) = (-x_1 + 1, y_1)
- B''(- (x_2 - 1), y_2) = (-x_2 + 1, y_2)
- C''(- (x_3 - 1), y_3) = (-x_3 + 1, y_3)
- D''(- (x_4 - 1), y_4) = (-x_4 + 1, y_4)
Now we compare these coordinates against the options A, B, C, and D to find the correct set of transformed coordinates.
To find the exact coordinates of transformed points, we would require the original shape's coordinates. However, we can determine the transformation effects based on signs of the x-coordinates and the y-values after transformation.
Given the nature of the possible answers, we can directly evaluate them based on the expected transformations:
- If we take any coordinates, translating to the left will decrease x-values by 1, and reflecting makes them negative, effectively flipping x-values and adjusting as necessary.
On examining the options, the only one that satisfies the transformation of left -1 and then reflecting (which typically increases the negative component by reversing it) when we analyze common values:
- Considering D (-2, -2), (-3, -2), (-5, -5), (-2, -5) match the general transformation pattern.
That concludes that the answer is likely D: (-2, -2), (-3, -2), (-5, -5), (-2, -5).