Question

If CDEF is reflected to C'D'E'F' then what is the line of reflection? Give the answer in the form of an equation.

C(-5,2)
D(-5,0)
E(-2,0)

Answer 1

To find the line of reflection for the shape CDEF, we first need to determine the coordinates of the points after reflection, C', D', and E', in order to identify the equation of the line of reflection.

Given the following points:
- C(-5, 2)
- D(-5, 0)
- E(-2, 0)

Assuming we are reflecting the points over the x-axis, then the coordinates of the reflected points would be:
- C'(-5, -2)
- D'(-5, 0)
- E'(-2, 0)

Next, we'll find a line that is the bisector of the segments connecting each original point with its corresponding reflected point because the line of reflection is the perpendicular bisector of those segments.

To find the midpoint and the slope:
1. For point C and C':
- Midpoint \( M_C \) of C and C' = \(\left( \frac{-5 + (-5)}{2}, \frac{2 + (-2)}{2} \right) = (-5, 0)\)

2. For point D and D':
- Midpoint \( M_D \) of D and D' = \(\left( \frac{-5 + (-5)}{2}, \frac{0 + 0}{2} \right) = (-5, 0)\)

3. For point E and E':
- Midpoint \( M_E \) of E and E' = \(\left( \frac{-2 + (-2)}{2}, \frac{0 + 0}{2} \right) = (-2, 0)\)

Now, since points D and D' remain on the same vertical line (x = -5), the line of reflection must also have points on x = -5. However, we must check for the points reflected.

The reflection line that bisects the height between C (at y = 2) and C' (at y = -2) must be y = 0, which means the line of reflection is the x-axis.

Therefore, the equation of the line of reflection is:

\[
y = 0
\]

This indicates that the reflection is happening across the x-axis.