https://file.aiquickdraw.com/mathbot/file/172568527521188j3wqgq.jpg

The task involves using the graph of triangle \( KLM \) to estimate \( \angle K \) and record the coordinates of the triangle vertices. Additionally, an algebraic representation for the triangle's reflection is needed.

### Step 1: Estimating \( \angle K \)
Observing the graph, \( \angle K \) appears to be an acute angle where line segment \( KL \) is nearly horizontal and \( KM \) slopes downwards. Estimating \( \angle K \) visually might suggest it is around 40-50 degrees. Exact measurement could be done using a protractor tool on the physical graph.

### Step 2: Recording Coordinates
The coordinates for the vertices of triangle \( KLM \) based on the graph are:
- \( K = (4, 2) \)
- \( L = (6, 2) \) (This point lies horizontally from \( K \), making \( KL \) horizontal.)
- \( M = (6, -1) \)

### Step 3: Algebraic Representation for Reflection
The reflection specified is over the \( y \)-axis. Reflecting over the \( y \)-axis means negating the \( x \)-coordinate of each point. Thus, the coordinates of the reflected triangle \( K'L'M' \) are:
- \( K' = (-4, 2) \)
- \( L' = (-6, 2) \)
- \( M' = (-6, -1) \)

The algebraic representation for the vertices after reflection is \( K'(-4, 2), L'(-6, 2), M'(-6, -1) \).

Would you like to explore this topic further or have any questions? Here are a few follow-up queries you might consider:

1. How to calculate the angles of a triangle using coordinates?
2. What properties of a triangle remain unchanged after reflection?
3. How to find the area of triangle \( KLM \) using its coordinates?
4. Can we determine the type of triangle \( KLM \) is based on its side lengths?
5. What are the implications of triangle reflections in geometry and real-life applications?

**Tip:** When reflecting points across an axis, only the coordinate perpendicular to that axis changes sign. This makes it straightforward to find the reflection if you know which axis you are reflecting over.

Reflect triangle JKL over the x-axis. Record the coordinates of the image and provide an algebraic representation of the reflection.

Learn how to reflect triangle JKL over the x-axis and find the new coordinates of the reflected image. This problem covers key concepts of coordinate geometry and geometric transformations, including reflection over the x-axis.

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