To determine the new coordinates of each point after the flood moves your house 4 blocks to the left and 2 blocks down, we need to apply the transformation to each point's coordinates. The transformation can be expressed as:
\[ (x_{\text{new}}, y_{\text{new}}) = (x_{\text{old}} - 4, y_{\text{old}} - 2) \]
This means we subtract 4 from the x-coordinate (indicating a move to the left) and subtract 2 from the y-coordinate (indicating a move down).
We will now apply this transformation to each point:
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Point A (2, 2): \[ A_{\text{new}} = (2 - 4, 2 - 2) = (-2, 0) \]
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Point B (0, 0): \[ B_{\text{new}} = (0 - 4, 0 - 2) = (-4, -2) \]
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Point C (0, 2): \[ C_{\text{new}} = (0 - 4, 2 - 2) = (-4, 0) \]
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Point D (-1, 3): \[ D_{\text{new}} = (-1 - 4, 3 - 2) = (-5, 1) \]
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Point E (-2, 2): \[ E_{\text{new}} = (-2 - 4, 2 - 2) = (-6, 0) \]
Now we can list the new coordinates for all points:
- New coordinates for A: \( (-2, 0) \)
- New coordinates for B: \( (-4, -2) \)
- New coordinates for C: \( (-4, 0) \)
- New coordinates for D: \( (-5, 1) \)
- New coordinates for E: \( (-6, 0) \)
Description of the Formal Transformation:
The formal transformation that occurred when the flood moved the house involved a shift in both the x and y coordinates of each point. Specifically, each point experienced:
- A horizontal shift of 4 units to the left, represented mathematically as subtracting 4 from the original x-coordinate.
- A vertical shift of 2 units downward, represented mathematically as subtracting 2 from the original y-coordinate.
Consequently, all original coordinates were adjusted accordingly, resulting in new positions that accurately depict the displacement caused by the flood. In simpler terms, we took every point in the original coordinate system and moved it left and down according to the flood's effects, leading to the new coordinates provided above.