Reflection across Vertical, Horizontal, and Oblique Lines

This applet demonstrates reflection in plane geometry. It dynamically illustrates the reflection of polygons, such as triangles and trapezoids, across vertical, horizontal, and arbitrary oblique lines. Users can visually observe the congruence between the original and reflected figures in terms of coordinates, side lengths, and angles, gaining a deeper understanding of geometric transformations and their algebraic representations in the coordinate plane. Through interactive manipulation, learners can drag vertices of the polygon or adjust the position and slope of the line of reflection to explore how each point maps to its image under different axes of symmetry. The applet highlights that reflections are rigid transformations, preserving distances and angle measures while reversing orientation. Students can compare corresponding coordinates before and after reflection: points reflected across a vertical line share the same y-coordinate while their x-coordinates are symmetric about the line; points reflected across a horizontal line share the same x-coordinate while their y-coordinates are symmetric about the line; and reflections across an oblique line follow a predictable algebraic pattern determined by the slope and intercept of the mirror line. This dynamic environment encourages exploration and discovery, allowing students to formulate conjectures about the properties of reflections and verify them experimentally. By engaging with the applet, learners develop both geometric intuition and algebraic reasoning skills, bridging the gap between visual geometry and coordinate algebra.