https://file.aiquickdraw.com/mathbot/file/1727992847168gxcjoy5w.jpg

Let's break this down step by step.

### 5.) Transformation (x, y) → (x - 5, y + 6)

The transformation rule is applied to each point of quadrilateral ABCD. We will subtract 5 from each x-coordinate and add 6 to each y-coordinate.

- **Point A (1, -4):**
  \[
  A' = (1 - 5, -4 + 6) = (-4, 2)
  \]
- **Point B (4, -4):**
  \[
  B' = (4 - 5, -4 + 6) = (-1, 2)
  \]
- **Point C (4, -2):**
  \[
  C' = (4 - 5, -2 + 6) = (-1, 4)
  \]
- **Point D (1, -2):**
  \[
  D' = (1 - 5, -2 + 6) = (-4, 4)
  \]

So, the coordinates for A', B', C', and D' after the transformation are:
- A'(-4, 2)
- B'(-1, 2)
- C'(-1, 4)
- D'(-4, 4)

### 6.) Transformation (x, y) → (x + 5, y - 8)

For this transformation, we add 5 to each x-coordinate and subtract 8 from each y-coordinate.

- **Point A (2, 1):**
  \[
  A' = (2 + 5, 1 - 8) = (7, -7)
  \]
- **Point B (5, 1):**
  \[
  B' = (5 + 5, 1 - 8) = (10, -7)
  \]
- **Point C (5, 6):**
  \[
  C' = (5 + 5, 6 - 8) = (10, -2)
  \]
- **Point D (2, 6):**
  \[
  D' = (2 + 5, 6 - 8) = (7, -2)
  \]

Thus, the coordinates for A', B', C', and D' after the transformation are:
- A'(7, -7)
- B'(10, -7)
- C'(10, -2)
- D'(7, -2)

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Would you like further clarification on any step or more details? Here are some related questions:

1. How can we determine whether a transformation is a translation, rotation, or reflection?
2. What is the difference between a dilation and a translation in geometry?
3. How would changing both x and y by negative values affect a shape's position?
4. How does the distance between points change under a simple translation?
5. Can you visualize how these transformations would shift the quadrilaterals on a coordinate plane?

**Tip:** When performing a translation, all points of a shape move by the same amount in the same direction, which preserves the shape and size of the figure.

Solve the transformations for points ABCD based on the given rules: (x - 5, y + 6) and (x + 5, y - 8).

Learn how to solve the coordinate transformation for quadrilateral ABCD using translation rules (x - 5, y + 6) and (x + 5, y - 8). Includes detailed steps for solving points A, B, C, and D. Suitable for students in Grades 7-9.

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