Question

You bought a house located at: A (2,3); B( 4,3); C(4,5); D(3,6); E(2,5)
a flood moves your house exactly 4 blocks to the left and two blocks down. Describe specifically the formal transformation that occurred when the flood moved your house.

Answer 1

To describe the formal transformation that occurred when the flood moved your house, we analyze the original coordinates of the house's vertices and how they change due to the movement caused by the flood.

Original coordinates of the house vertices:
- A(2, 3)
- B(4, 3)
- C(4, 5)
- D(3, 6)
- E(2, 5)

The transformation specified indicates that the house is moved 4 blocks to the left and 2 blocks down.

**Transformation Steps:**
1. **Moving 4 blocks to the left:** This action subtracts 4 from the x-coordinate of each vertex.
2. **Moving 2 blocks down:** This action subtracts 2 from the y-coordinate of each vertex.

**Formal Transformation:**
The transformation can be expressed as:
\[
(x, y) \rightarrow (x - 4, y - 2)
\]

**Applying the Transformation:**
Now, we apply this transformation to each vertex:

- For point A(2, 3):
\[
A' = (2 - 4, 3 - 2) = (-2, 1)
\]

- For point B(4, 3):
\[
B' = (4 - 4, 3 - 2) = (0, 1)
\]

- For point C(4, 5):
\[
C' = (4 - 4, 5 - 2) = (0, 3)
\]

- For point D(3, 6):
\[
D' = (3 - 4, 6 - 2) = (-1, 4)
\]

- For point E(2, 5):
\[
E' = (2 - 4, 5 - 2) = (-2, 3)
\]

**New Coordinates After Transformation:**
- A'(-2, 1)
- B'(0, 1)
- C'(0, 3)
- D'(-1, 4)
- E'(-2, 3)

This transformation is a translation, specifically translating the house 4 units left and 2 units down in a Cartesian coordinate system.