Question

A flood moves your house exactly 4 blocks to the left and 2 blocks down
The new coordinates are A(-2,0), B (4, 2), C(O, 2) , D(-2, 3) E(-2, 2)
Describe Specifically the formal transformation that occured when the flood moved the house. 

Answer 1

Make it easier to understand and make it sound like an 8th grader wrote it

Answer 2

To describe the formal transformation that occurred when the flood moved the house from its original position to the new position, we can model the transformation using a translation in the coordinate plane.

1. **Original Coordinates**: Let's denote the original coordinates of the house as \((x, y)\).
2. **Transformation Description**:
- The flood moves the house **4 blocks to the left**. This means we subtract 4 from the x-coordinate: \(x' = x - 4\).
- The flood also moves the house **2 blocks down**. This means we subtract 2 from the y-coordinate: \(y' = y - 2\).
3. **Transformation Vector**: We can express this transformation as:
\[
(x', y') = (x - 4, y - 2)
\]
This can be represented using a translation vector \(\mathbf{T} = (-4, -2)\).

**Formal Transformation**: Thus, the formal transformation is:
\[
T(x, y) = (x - 4, y - 2)
\]

Now let's apply this transformation to determine the output vertices based on the original coordinates.

### Finding New Coordinates
Assuming we perform the transformation on different points:
- For point A(-2, 0):
\[
A' = (-2 - 4, 0 - 2) = (-6, -2)
\]
- For point B(4, 2):
\[
B' = (4 - 4, 2 - 2) = (0, 0)
\]
- For point C(0, 2):
\[
C' = (0 - 4, 2 - 2) = (-4, 0)
\]
- For point D(-2, 3):
\[
D' = (-2 - 4, 3 - 2) = (-6, 1)
\]
- For point E(-2, 2):
\[
E' = (-2 - 4, 2 - 2) = (-6, 0)
\]

### Conclusion
The formal transformation due to the flood moving your house is represented by the translation:
\[
T(x, y) = (x - 4, y - 2)
\]
This transformation moves every point 4 blocks to the left and 2 blocks down in the coordinate plane.