Follow the guided instructions below to create the line of reflection that would map the pink figure onto the blue figure.

Question

Now write the slope of the line of reflection and any dotted line.
x
y
x
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Slope of one of the dotted lines:

Slope of the line of reflection:

Answer 1

To create the line of reflection that maps a pink figure onto a blue figure, follow these steps:

1. Identify Points: Identify corresponding points on the pink figure and the blue figure. Let's say point \( A \) on the pink figure corresponds to point \( A' \) on the blue figure.

2. Midpoint Calculation: Calculate the midpoint \( M \) between points \( A \) and \( A' \). This midpoint will lie on the line of reflection. The coordinates of the midpoint \( M \) can be calculated as: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] where \( (x_1, y_1) \) are the coordinates of \( A \) and \( (x_2, y_2) \) are the coordinates of \( A' \).

3. Slope Calculation: Next, calculate the slope \( m_{AA'} \) of the segment connecting points \( A \) and \( A' \): \[ m_{AA'} = \frac{y_2 - y_1}{x_2 - x_1} \]

4. Slope of the Line of Reflection: The slope of the line of reflection \( m_r \) will be the negative reciprocal of the slope \( m_{AA'} \): \[ m_r = -\frac{1}{m_{AA'}} \]

5. Dotted Lines: Draw dotted lines from points \( A \) to \( A' \) and from \( A' \) to \( M \) to visually represent this.

Now, let’s define the slopes based on your specific figures:

• Slope of one of the dotted lines: This will be the slope \( m_{AA'} \) that you calculated in step 3.

• Slope of the line of reflection: This will be \( m_r \) calculated in step 4.

You would need the coordinates of specific points to provide numerical values for the slopes. If you provide the coordinates of the points, I could help you calculate them.