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Let's go over each question step-by-step.

### Problem 6:
You need to find the image of the triangle reflected across the mirror line \( m \). Reflection means each point of the triangle should be equidistant from \( m \) on the opposite side. Let’s analyze each option:
1. **(a)**: The vertices of the triangle in option (a) do not seem to be reflected correctly, as their orientation is not a mirror image.
2. **(b)**: This option also does not align with the mirror line.
3. **(c)**: This shows an accurate mirror image of the original triangle across line \( m \). The distances and orientation seem correct.
4. **(d)**: This option is also incorrect for a reflection across \( m \).

**Answer for Problem 6:** The correct answer is **(c)**.

### Problem 7:
In this problem, you need to find the image of triangle \( ABC \) after a dilation with center \( O \) and a scale factor of 3. Dilation means that each point \( A \), \( B \), and \( C \) should be three times farther from \( O \) than they were initially, maintaining the same direction from \( O \).

1. **(a)**: Triangle is the correct shape, but the distance from \( O \) isn’t scaled by 3.
2. **(b)**: This triangle is similarly too close to \( O \) and does not show the correct scaling.
3. **(c)**: The vertices appear correctly scaled by a factor of 3, making this a potential answer.
4. **(d)**: This triangle does not reflect a scale factor of 3 from \( O \) either.

**Answer for Problem 7:** The correct answer is **(c)**.

Would you like a more detailed explanation, or have any questions about these steps?

### Relative Questions:
1. What is the rule for reflecting a point across a line?
2. How do you determine the coordinates of a point after a reflection?
3. What is the effect of a dilation with a fractional scale factor?
4. How would a reflection change if the mirror line is vertical?
5. How does changing the center of dilation affect the resulting image?

**Tip:** When performing a reflection, ensure each point of the image is directly across from the original on the opposite side of the mirror line, maintaining equal distances.

Find the image of the given figure under a reflection across the mirror line m, and find the image of triangle ABC for a dilation with center O and scale factor 3.

Learn how to find the reflected image of a triangle across a line and perform a dilation transformation with center and scale factor. This problem covers key concepts of reflections and dilations, making it ideal for students in Grades 8-10.

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