To determine the new coordinates for the house after the flood moves it, we start with the original coordinates (x, y). The movement can be described as follows:
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The house moves 4 blocks to the left. This means we are subtracting 4 from the x-coordinate: \[ \text{New x-coordinate} = x - 4 \]
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The house moves 2 blocks down. This means we are subtracting 2 from the y-coordinate: \[ \text{New y-coordinate} = y - 2 \]
Overall, the transformation of the coordinates can be expressed as: \[ \text{New Coordinates} = (x - 4, y - 2) \]
Now, if we assume the original coordinates of the house are given, for example, let's assume those coordinates are (x, y). We can notate them as follows:
- Given Original Coordinates (for example): (x, y)
After the transformation due to the flood:
- New Coordinates: (x - 4, y - 2)
Now, let's analyze the options provided in the problem. Since we do not have the original coordinates provided, we'll review the possible transformed outcomes considering various initial coordinates. For the response to the question regarding the formal transformation that occurred:
Formal Transformation Description
The formal transformation that occurred when the flood moved the house can be described mathematically as a vector translation in the coordinate plane. It can be defined using the following steps:
- The translation of the house is represented by the vector \( T(-4, -2) \), where:
- -4 is the movement to the left along the x-axis (negative direction).
- -2 is the movement down along the y-axis (also a negative direction).
This transformation results in a shift of each point in the original coordinate set by subtracting 4 from the x-values and 2 from the y-values. Thus, if the original coordinates of the house were (x, y), the new coordinates after the transformation will be recalibrated to (x - 4, y - 2).
This type of transformation is typically described as a translation, affecting the position of the house without altering its dimensions or orientation.
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