To identify the transformation that maps triangle \( \triangle ABC \) to triangle \( \triangle A"B"C" \), we need to analyze the relationship between the corresponding points \( A, B, C \) and \( A", B", C" \).
There are several types of transformations that can be applied to a triangle, including:
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Translation: This moves every point a fixed distance in a specified direction. If \( \triangle A"B"C" \) is simply a shifted version of \( \triangle ABC \), then the transformation is a translation.
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Rotation: This turns the triangle around a fixed point (the center of rotation). If \( \triangle A"B"C" \) is rotated around a point, then the transformation would be a rotation.
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Reflection: This flips the triangle over a line (the axis of reflection). If \( \triangle A"B"C" \) is a mirror image of \( \triangle ABC \), the transformation is a reflection.
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Dilation: This changes the size of the triangle while preserving its shape. If \( \triangle A"B"C" \) is larger or smaller than \( \triangle ABC \) but has the same shape, the transformation is a dilation.
To determine the specific transformation, we would typically need the coordinates of the points \( A, B, C \) and \( A", B", C" \). By comparing the coordinates, we could identify whether the transformation is a translation, rotation, reflection, or dilation.
If you have the coordinates, please provide them, and I can help identify the specific transformation!