Question

Translate and label each vertex

Pre image points are:
A (3, 2)
В(6, 3)
C(7,1)

Image points are :
A’ ( -4,2)
B’( -1,3)
C’ (0,2)

Answer 1

To translate and label each vertex, we need to specify the translation for each point based on the given pre-image and image points.

1. **Translate each vertex**: The translation can be found by looking at how each original point (pre-image) is moved to its new position (image).

2. **Calculate the translation vector**:
- For point A:
- Original A (3, 2) moves to A’ (-4, 2)
- Translation: A' = A + T => T = A' - A = (-4, 2) - (3, 2) = (-4 - 3, 2 - 2) = (-7, 0)
- For point B:
- Original B (6, 3) moves to B’ (-1, 3)
- Translation: B' = B + T => T = B' - B = (-1, 3) - (6, 3) = (-1 - 6, 3 - 3) = (-7, 0)
- For point C:
- Original C (7, 1) moves to C’ (0, 2)
- Translation: C' = C + T => T = C' - C = (0, 2) - (7, 1) = (0 - 7, 2 - 1) = (-7, 1)

From this calculation, we see that the translation vector is not uniform, meaning the translation effects depend on each specific vertex.

Thus the translations from the pre-image to image points are as follows:

**Translation for each point**:
- A: Translate by (-7, 0)
- B: Translate by (-7, 0)
- C: Translate by (-7, 1)

**Summary of Points**:
- A (3, 2) translates to A’ (-4, 2)
- B (6, 3) translates to B’ (-1, 3)
- C (7, 1) translates to C’ (0, 2)

Here are the labeled translations:

1. **A -> A'**:
Pre-image A (3, 2) ➔ Image A' (-4, 2)
**Translation vector**: (-7, 0)

2. **B -> B'**:
Pre-image B (6, 3) ➔ Image B' (-1, 3)
**Translation vector**: (-7, 0)

3. **C -> C'**:
Pre-image C (7, 1) ➔ Image C' (0, 2)
**Translation vector**: (-7, 1)

Thus, each vertex has been translated and labeled based on their respective transformations.