https://file.aiquickdraw.com/mathbot/file/17301198323014fn532oe.jpg

To analyze the similarity between triangles \( PQR \) and \( JKL \), let's examine the transformation options provided:

1. **Reflection and Dilation**:
   - The first two options suggest reflecting \( \triangle PQR \) across the \( x \)-axis, then scaling it either by a factor of 3 or \( \frac{1}{3} \). 
   - Reflecting \( \triangle PQR \) across the \( x \)-axis would flip it vertically, and a dilation would change its size. Scaling by 3 would make it larger, while \( \frac{1}{3} \) would make it smaller.

2. **Rotation and Dilation**:
   - The last two options involve rotating \( \triangle PQR \) 90° counterclockwise around the origin, then dilating it by either a scale factor of 3 or \( \frac{1}{3} \).
   - Rotating 90° counterclockwise around the origin would change the orientation of \( \triangle PQR \), and the dilation factor would affect its size similarly as in the reflection case.

### Determining the Correct Answer
By examining the graph:
- \( \triangle JKL \) appears to be similar in shape but not identical in size to \( \triangle PQR \), suggesting a scale change.
- The orientation difference implies either a rotation or a reflection.

**Correct Answer**: The transformation that best describes the similarity is the fourth option:
> \( \triangle JKL \) is obtained by rotating \( \triangle PQR \) 90° counterclockwise around the origin and then dilating the resulting triangle by a scale factor of \( \frac{1}{3} \).

Would you like further details on transformations, or have additional questions?

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**Related Questions:**

1. How do you determine the scale factor for dilation in similar triangles?
2. What properties make two triangles similar?
3. How does a 90° counterclockwise rotation affect the coordinates of points?
4. What are other ways to identify transformations on a coordinate plane?
5. How does reflection differ from rotation in terms of resulting shapes?

**Tip:** To confirm similarity, compare corresponding angles and the proportionality of sides after the transformation.

Which statement correctly describes why the two triangles are similar?

Identify the correct transformation to explain the similarity between triangles PQR and JKL in a coordinate plane. This problem explores geometry concepts, including rotations, dilations, reflections, and similarity transformations. Ideal for Grade 8 math students.

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