$$ \mathrm{D}(-4,2), \mathrm{E}(-4,4), \mathrm{F}(-7,4), \mathrm{G}(-6,2) $$ Translate 1 unit right and 7 units down

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To translate the points **1 unit to the right** and **7 units down**, you need to adjust each point's coordinates as follows:

- **Right by 1 unit**: Add 1 to the x-coordinate.
- **Down by 7 units**: Subtract 7 from the y-coordinate.

Let's apply this transformation to each point:

1. **Point D $$(-4, 2)$$**
   $$
   D' = (-4 + 1,\ 2 - 7) = (-3,\ -5)
   $$

2. **Point E $$(-4, 4)$$**
   $$
   E' = (-4 + 1,\ 4 - 7) = (-3,\ -3)
   $$

3. **Point F $$(-7, 4)$$**
   $$
   F' = (-7 + 1,\ 4 - 7) = (-6,\ -3)
   $$

4. **Point G $$(-6, 2)$$**
   $$
   G' = (-6 + 1,\ 2 - 7) = (-5,\ -5)
   $$

**Translated Coordinates:**
- $$ D'(-3,\ -5) $$
- $$ E'(-3,\ -3) $$
- $$ F'(-6,\ -3) $$
- $$ G'(-5,\ -5) $$

---

**Visualization:**

If you plot the original and translated points on a coordinate plane, you'll see that each new point has moved 1 unit to the right and 7 units downward from its original position.

![Translation of Points](https://i.imgur.com/translated_points.png)

*(Note: Replace the image link with an actual graph if needed.)*
After translating 1 unit to the right and 7 units down, the new coordinates are: - D'(-3, -5) - E'(-3, -3) - F'(-6, -3) - G'(-5, -5)

\( \mathrm{D}(-4,2), \mathrm{E}(-4,4), \mathrm{F}(-7,4), \mathrm{G}(-6,2) \) Translate 1 unit right and 7 units down

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