A figure is translated 4 units left and 2 units up.  If the domain (or pre-image) of the coordinate transformation (1, -5), (−3, 7), (−1, 3), what is the range (or image)?

pick one:

(-3, -7), (-7, 5), (-5, 5)

(5, -3), (1, 9), (3, 5)

(-3, -3), (-7, 9), (-5, 5)

(3, 7), (-7, 9), (-5, 5)

To determine the range (or image) after translating the given points, we apply the translation to each of the coordinates. The translation is defined as 4 units left and 2 units up.

### Translation Steps:
- **4 units left**: Subtract 4 from the x-coordinate.
- **2 units up**: Add 2 to the y-coordinate.

Let's apply this to each point in the domain:

1. **Original point** \((1, -5)\):
   - New x-coordinate: \(1 - 4 = -3\)
   - New y-coordinate: \(-5 + 2 = -3\)
   - Translated point: \((-3, -3)\)

2. **Original point** \((-3, 7)\):
   - New x-coordinate: \(-3 - 4 = -7\)
   - New y-coordinate: \(7 + 2 = 9\)
   - Translated point: \((-7, 9)\)

3. **Original point** \((-1, 3)\):
   - New x-coordinate: \(-1 - 4 = -5\)
   - New y-coordinate: \(3 + 2 = 5\)
   - Translated point: \((-5, 5)\)

### Translated Points (Range):
The resulting range after translation is \((-3, -3)\), \((-7, 9)\), and \((-5, 5)\).

### Matching with Options:
The correct range from the options is \(\boxed{(-3, -3), (-7, 9), (-5, 5)}\), which is the 3rd option.

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Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the effect of translating a figure on its shape and size?
2. How would a translation 3 units right and 5 units down affect the coordinates?
3. What is the difference between a translation and a rotation in coordinate transformations?
4. Can a translation change the orientation of a figure?
5. How would the translation affect a point located at the origin \((0, 0)\)?

**Tip:** When translating points, always remember to adjust both the x and y coordinates accordingly, depending on the direction and magnitude of the translation.

Explore how to translate points in a coordinate plane 4 units left and 2 units up. Understand the effect of this transformation on given points (1, -5), (-3, 7), and (-1, 3). Suitable for Grades 7-9.

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