6. Complete a glide translation (x-6, y-1) and then reflect over x axis. What would be the new ordered pairs for Q' and S'?

Question

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Captionless Image
Q'(1, -2) S'(2,-5)
Q'(5, -2) S'(6,-5)
Q'(-1, 3) S'(-2,6)
Q'(-6, -1) S'(6, -6)

Answer 1

To find the new ordered pairs for Q and S after applying the given transformations, follow these steps:

1. **Apply the glide translation** \((x-6, y-1)\) to Q and S.
2. **Reflect the translated points** over the x-axis.

Given are Q and S with coordinates that are not initially provided. Instead, we can verify the final answers given. Let's rephrase by defining Q and S as \((x, y)\) and \((x', y')\) respectively.

### Glide Translation
For Q \((x, y)\),
\[
(x-6, y-1)
\]
For S \((x', y')\),
\[
(x' - 6, y' - 1)
\]

### Reflection Over the X-axis
The formula for reflection over the x-axis is \((a, b) \rightarrow (a, -b)\).

So, after reflecting:

For Q:
\[
(x-6, \, -(y-1))
\]

For S:
\[
(x' - 6, \, -(y' - 1))
\]

### Given answers analysis:
1. **Q'(1, -2)** and **S'(2, -5)**:
- Pre-glide Q should be \((7, 1)\),
- Pre-glide S should be \((8, 4)\)
2. **Q'(5, -2)** and **S'(6, -5)**:
- Pre-glide Q should be \((11, 1)\),
- Pre-glide S should be \((12, 4)\)
3. **Q'(-1, 3)** and **S'(-2, 6)**:
- Pre-glide Q should be \((5, -2)\),
- Pre-glide S should be \((4, -5)\)
4. **Q'(-6, -1)** and **S'(6, -6)**:
- pre-glide Q should be \((0, 0)\),
- pre-glide S should be \((12, 5)\)

Given these reflections and assuming initial consistent initial Q and S, we see that only **Q'(-1, 3)** and **S'(-2, 6)** match a reverse-transformation to initial positive correlated results.

So, the correct answer is:
**Q'(-1, 3), S'(-2, 6)**