https://file.aiquickdraw.com/mathbot/file/1726752188731c8i4i9q0.jpg

Let's go step by step through the transformations for point **C**.

1. **Reflection across the x-axis**:
   - The original coordinates of point **C** are \((-3, 0)\).
   - When reflecting across the x-axis, the y-coordinate changes its sign, but the x-coordinate remains the same.
   - So, after reflecting across the x-axis, the new coordinates of point **C'** will be \((-3, 0)\) (since the y-coordinate is 0, the reflection doesn't change it).

2. **Translation 5 units to the left**:
   - Translating left by 5 units means subtracting 5 from the x-coordinate.
   - The x-coordinate of **C'** is \(-3\), so:
     \[
     -3 - 5 = -8
     \]
   - The y-coordinate remains the same (0).

Thus, the coordinates of **C''** after both transformations are \((-8, 0)\). However, this isn't listed as one of the options. 

Looking back at the options, it seems like there might be a mistake in the problem's options, or another detail might need clarification. Would you like to ask for clarification or discuss further?

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Here are 5 questions to extend understanding:
1. How do transformations affect other points in the triangle?
2. What happens when you reflect over the y-axis instead?
3. How would you translate a point 5 units right instead of left?
4. What if the reflection was over the line \(y = x\)?
5. How would the transformation change if the translation was vertical?

**Tip:** Always double-check transformations visually by plotting the points on graph paper!

Perform the given sequence of transformations: Reflect across the x-axis. Translate 5 units left. What are the coordinates of C''?

This problem involves performing a reflection across the x-axis followed by a translation 5 units to the left. Understand how to apply coordinate transformations to points on the graph. Suitable for students in Grades 6-8.

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