Question

The vertices of triangle ABC are A(-5,4), B(-2,3), and C(-2,2). If triangle ABC is reflected across the line y= -2 to produce the image of triangle A'B'C'. What are the coordinates for the vertex C'

Answer 1

To find the coordinates of vertex \( C' \) after reflecting point \( C(-2, 2) \) across the line \( y = -2 \), we can use the following steps:

1. **Identify the line of reflection**: The line \( y = -2 \) is a horizontal line.

2. **Calculate the distance from point C to the line**:
- The \( y \)-coordinate of point \( C \) is \( 2 \).
- The line \( y = -2 \) has a \( y \)-coordinate of \( -2 \).
- The distance from point \( C \) to the line is:
\[
2 - (-2) = 2 + 2 = 4
\]

3. **Reflect point \( C \)**:
- To reflect the point across the line, we move the same distance on the opposite side. Since the distance is \( 4 \), we subtract this distance from the line \( y = -2 \):
\[
-2 - 4 = -6
\]

4. **Determine the new coordinates**:
- The \( x \)-coordinate of point \( C \) remains the same because the reflection is across a horizontal line.
- Therefore, the coordinates of \( C' \) after reflection are:
\[
C' = (-2, -6)
\]

Thus, the coordinates of vertex \( C' \) are \(\boxed{(-2, -6)}\).