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.