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 \(\boxed{(-2, -6)}\).