Question

Your house is located at A (2,2), B (4,2), C (4,4), D (3,5), and E (2,4). A flood moves your house exactly 4 blocks to the left and 2 blocks down.Describe specifically the formal transformation that occurred when the flood moved your house

Answer 1

To describe the formal transformation of your house's location due to the flood, we need to represent the movement mathematically as a translation.

Your house's original coordinates are given as A(2,2), B(4,2), C(4,4), D(3,5), and E(2,4). The flood moves your house **4 blocks to the left** and **2 blocks down**.

1. **Movement to the left** means subtracting from the x-coordinate.
- Moving left 4 blocks: \( x' = x - 4 \)

2. **Movement downward** means subtracting from the y-coordinate.
- Moving down 2 blocks: \( y' = y - 2 \)

Therefore, the transformation can be represented as:
\[
(x', y') = (x - 4, y - 2)
\]

Now we can apply this transformation to each of the original coordinates of points A, B, C, D, and E:

1. For point A(2,2):
- \( A' = (2 - 4, 2 - 2) = (-2, 0) \)

2. For point B(4,2):
- \( B' = (4 - 4, 2 - 2) = (0, 0) \)

3. For point C(4,4):
- \( C' = (4 - 4, 4 - 2) = (0, 2) \)

4. For point D(3,5):
- \( D' = (3 - 4, 5 - 2) = (-1, 3) \)

5. For point E(2,4):
- \( E' = (2 - 4, 4 - 2) = (-2, 2) \)

Thus, the formal transformation applied to your house’s coordinates due to the flood is defined by the translation:
\[
T: (x, y) \to (x - 4, y - 2)
\]
resulting in the new coordinates:
- \( A'(-2, 0) \)
- \( B'(0, 0) \)
- \( C'(0, 2) \)
- \( D'(-1, 3) \)
- \( E'(-2, 2) \)