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We are given the translated vertices of triangle ABC after a translation of 3 units left and 8 units up. The translated triangle has vertices \( A'(1, -5) \), \( B'(1, -7) \), and \( C'(7, -6) \). We are tasked with finding the original coordinates of point \( C \).

### Translation Information:
- Moving left by 3 points means subtracting 3 from the x-coordinates.
- Moving up by 8 points means adding 8 to the y-coordinates.

### Reversing the Translation:
To find the original coordinates of point \( C \) (denoted as \( C(x, y) \)), we need to reverse the translation:
- For the x-coordinate: Add 3 to \( C'(7, -6) \)'s x-coordinate: \( 7 + 3 = 10 \).
- For the y-coordinate: Subtract 8 from \( C'(7, -6) \)'s y-coordinate: \( -6 - 8 = -14 \).

Thus, the original coordinates of point \( C \) are \( (10, -14) \).

Let me know if you'd like more details or if you have any questions!

Here are 5 related questions:
1. What would be the coordinates of point \( A \) before translation?
2. What is the original location of point \( B \)?
3. How can you generalize translation for other transformations?
4. How would a reflection across the x-axis change the coordinates of triangle ABC?
5. How would a dilation centered at the origin affect the triangle's vertices?

**Tip:** When reversing a transformation, apply the opposite operation to each coordinate.

Triangle ABC is translated 3 points left and 8 points up. The mapped triangle has vertices A'(1, -5), B'(1, -7), and C'(7, -6). Find the coordinates of point C.

Solve a geometry problem involving translations in the coordinate plane. Triangle ABC is translated 3 points left and 8 points up. Find the original coordinates of point C with a detailed step-by-step solution.

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