Final answer:
To find the reflected coordinates of rhombus KLMN over the line y = -2, calculate the distance each vertex is from y = -2 and place the reflected point the same distance on the opposite side. The coordinates K'(-3,-6), L'(1,-8), M'(-1,-4), and N'(-5,-2) are obtained.
Step-by-step explanation:
The student asks for the coordinates of the vertices of rhombus KLMN after reflecting each point over the line y = -2. To find the reflected coordinates, we need to determine how far each vertex is vertically from the line y = -2 and then place the reflected point the same distance on the opposite side of the line.
For vertex K(-3,2), the distance to the line y = -2 is 4 units (from 2 to -2). The reflected point K' will be 4 units below y = -2, which is at y = -6. So, K'( -3,-6).
Applying the same method to the other vertices:
- For L(1,4), L' is 4 + 2 = 6 units below the line, so at y = -8. Thus, L'(1, -8).
- For M(-1,0), M' is 2 units below the line, so at y = -4. Thus, M'(-1, -4).
- For N(-5,-2), as it lies on the line of reflection, it remains unchanged. Thus, N'(-5, -2).
The final reflected coordinates are:
- K' (-3,-6)
- L' (1,-8)
- M' (-1,-4)
- N' (-5,-2)