https://file.aiquickdraw.com/mathbot/file/1729513785394mwr10rlk.jpg

The image shows a triangle after a translation where the transformation rule is given as \((x, y) \rightarrow (x-2, y-4)\). We are tasked with finding the pre-images (original coordinates before translation) of points \(A'\), \(B'\), and \(C'\), which are shown after the transformation.

To reverse the translation, we add 2 to the x-coordinate and 4 to the y-coordinate of each image point.

1. **Point A'** has coordinates \((-4, -2)\).
   - Pre-image of A: \((-4 + 2, -2 + 4) = (-2, 2)\).

2. **Point B'** has coordinates \((-3, -1)\).
   - Pre-image of B: \((-3 + 2, -1 + 4) = (-1, 3)\).

3. **Point C'** has coordinates \((-2, -4)\).
   - Pre-image of C: \((-2 + 2, -4 + 4) = (0, 0)\).

Now, let's match these pre-images with the available choices:

- For \(A\), the pre-image is \((-2, 0)\).
- For \(B\), the pre-image is \((1, 2)\).
- For \(C\), the pre-image is \((0, 0)\).

Would you like more detailed clarification on the transformation process?

Here are 5 follow-up questions for practice:

1. How would you find the pre-image if the translation was \((x + 3, y - 5)\)?
2. What is the difference between a translation and a reflection in geometry?
3. Can you describe the rule for translating a point by a vector \((h, k)\)?
4. What happens to the coordinates of a point after reflecting over the x-axis?
5. If the translation rule was \((x + 4, y + 7)\), what would the pre-images of the points be?

**Tip**: For translations, reversing the operation means using the opposite sign of the given translation rule!

The picture shows the IMAGE after a Translation of (x, y) ---> (x - 2, y - 4). Name the Pre-Image of A, B, C (in this order).

Learn how to find the pre-images of points A, B, and C after a translation of (x - 2, y - 4) on a coordinate plane. This problem covers the basics of geometric transformations, including how to reverse a translation by adjusting the coordinates accordingly.

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