Triangle ABC has vertices at A(−4, 3), B(0, 5), and C(−2, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down.


To determine the coordinates of the vertices of triangle \(ABC\) after it is translated 4 units down, we apply the following translation rule:

- For each vertex \((x, y)\), the new coordinates will be:
  \[
  (x', y') = (x, y - 4)
  \]
  This is because a downward translation reduces the \(y\)-coordinate by 4 units while the \(x\)-coordinate remains unchanged.

### Step-by-Step Translation for Each Vertex:

1. **Vertex \( A(-4, 3) \):**
   \[
   A' = (-4, 3 - 4) = (-4, -1)
   \]

2. **Vertex \( B(0, 5) \):**
   \[
   B' = (0, 5 - 4) = (0, 1)
   \]

3. **Vertex \( C(-2, 0) \):**
   \[
   C' = (-2, 0 - 4) = (-2, -4)
   \]

### Final Coordinates of Triangle \( A'B'C' \):

- \( A'(-4, -1) \)
- \( B'(0, 1) \)
- \( C'(-2, -4) \)

These are the vertices of triangle \( A'B'C' \) after the preimage is translated 4 units down.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How would the translation change if the figure were moved 3 units to the right?
2. What is the effect of translating a figure both vertically and horizontally at the same time?
3. How do you describe a translation as a vector?
4. How does translation affect the area of a geometric figure?
5. What happens to the slopes of the sides of a triangle after a translation?

**Tip:** Translations preserve the size and shape of a figure; only its position changes. The figure remains congruent to the preimage.

Learn how to translate triangle ABC with vertices at A(-4, 3), B(0, 5), and C(-2, 0) 4 units down. Understand the effect of downward translation on triangle vertices using coordinate geometry. Suitable for Grades 7-9.

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