Question

Постройте фигуру,в которую перейдит трапеция при осевой симметрии относительно произвольной прямой

Answer 1

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Answer 2

Building a Figure with Trapezoid and Axis of Symmetry

To build a figure into which a trapezoid transitions under axial symmetry with respect to an arbitrary line, we can follow these steps:

1. Start with a Trapezoid: - Begin with a trapezoid, which is a quadrilateral with at least one pair of parallel sides. - The trapezoid can be represented by the points A, B, C, and D, where AB and CD are the parallel sides.

2. Identify the Axis of Symmetry: - Choose an arbitrary line as the axis of symmetry for the trapezoid.

3. Apply Axial Symmetry: - Reflect each point of the trapezoid across the chosen axis of symmetry. - For each point P(x, y), the reflected point P'(-x, y) will be equidistant from the axis of symmetry.

4. Construct the Reflected Trapezoid: - Connect the reflected points to form the new trapezoid, which is the image of the original trapezoid under axial symmetry.

5. Final Result: - The resulting figure will be the reflected trapezoid, which has undergone a transition due to the axial symmetry with respect to the chosen line.

For a visual representation and further details, please refer to the provided sources for a more comprehensive understanding of this geometric transformation.