Reflecting a quadrilateral across line m involves identifying corresponding points, determining displacement, applying the displacement rule, and checking for accuracy. Maintaining the original shape and orientation is crucial for a successful reflection.
The rule for the reflection of quadrilateral ABCD across line m.
Identify Corresponding Points:
Each vertex of the quadrilateral will have a corresponding point on the other side of the line after the reflection. These corresponding points are named with primes: A', B', C', and D'.
Determine the Displacement:
For each vertex, determine its distance and direction from the reflection line (m). This distance and direction will be the same for the corresponding point on the other side, but with the direction flipped.
For example, if point A is 3 units to the right and 2 units above line m, then point A' will be 3 units to the right and 2 units below line m.
Apply the Displacement Rule:
Use the displacement information from step 2 to find the coordinates of each reflected point. For example, if A is at (5, 4), then A' will be at (5, 2).
Check and Adjust:
Once you have the coordinates for all reflected points, plot them on the graph and connect them to form the reflected quadrilateral. Make sure the reflected figure maintains the same overall shape and orientation as the original quadrilateral. If not, check your calculations and adjust accordingly.