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To find the **equation of the line of reflection**, we can use the **point-slope form** of a line equation. Given that we already know:

- The **slope** of the line of reflection is \( 1 \).
- The line of reflection passes through the **origin** (point \( (0, 0) \)).

The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.

Since the line passes through \( (0, 0) \) and the slope is \( 1 \), we plug these values into the equation:
\[
y - 0 = 1(x - 0)
\]
Simplifying this equation, we get:
\[
y = x
\]

Thus, the **equation of the line of reflection** is:
\[
y = x
\]

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Would you like to explore this further or need any additional clarifications?

Here are 5 related questions for deeper understanding:
1. How does the equation of the line change if the reflection line doesn’t pass through the origin?
2. What is the general form of the equation of a line?
3. How do we reflect a point across the line \( y = x \)?
4. Can the line of reflection have a slope other than 1 or -1 for different transformations?
5. How can you determine if two figures are congruent after reflection?

**Tip:** When reflecting shapes across a line, always check the relationship between the original and reflected points, ensuring distances are maintained and perpendiculars drawn to the line of reflection are equal.

Now write the slope of the line of reflection and any dotted line.

Explore how to determine the equation of the line of reflection with a slope of 1 and how it applies to geometric transformations on a coordinate plane. This example uses the point-slope form of a line, demonstrating a fundamental concept in high school geometry.

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