This problem asks for a reflection of the triangle across two lines, $m$ and $n$, and then requires you to describe the overall transformation.

Steps to solve:

1. Reflect across line $m$:

   • First, reflect the triangle $\triangle QRT$ across line $m$. The reflection will result in a new triangle on the other side of line $m$ with an identical shape and size but mirrored orientation.

2. Reflect across line $n$:

   • Next, take the reflected image from step 1 and reflect it again across line $n$. Since the angle between line $m$ and line $n$ is $35^\circ$, the new image will be at another mirrored orientation but on the opposite side of line $n$.

Identifying the single transformation:

• The result of two reflections can be described as a rotation. Specifically:
  • Reflecting across two intersecting lines (lines $m$ and $n$) is equivalent to a rotation about the point of intersection of the two lines.
  • The angle of rotation is twice the angle between the two lines. Since the angle between $m$ and $n$ is $35^\circ$, the total rotation is $2 \times 35^\circ = 70^\circ$.
  • Therefore, the transformation that maps the preimage (the original triangle) onto the final image is a rotation of 70 degrees around the intersection point of lines $m$ and $n$.

Would you like more details or have any questions about this solution?

Relative Questions:

1. How do you reflect a point across a line in a coordinate plane?
2. What is the general rule for finding the result of two reflections across intersecting lines?
3. How does the angle between two lines affect the result of double reflections?
4. How would the transformation change if the lines $m$ and $n$ were parallel?
5. Can you describe the process of determining the center of rotation?

Tip:

When two reflections are performed across intersecting lines, the final transformation is always a rotation, and the angle of rotation is double the angle between the lines.