To determine which single transformation maps triangle ABC onto triangle A'B'C', we need to analyze the relationship between the two triangles.
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Dilation: This transformation changes the size of a figure but keeps its shape. If A'B'C' is a scaled version of ABC, this could be a potential transformation.
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Rotation about the origin: This transformation turns the figure around a specific point (the origin in this case). If triangle A'B'C' is the same size as ABC and appears as if it has been rotated around the origin, then this is the correct transformation.
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Translation: This transformation shifts the whole figure in a specific direction. If both triangles are the same size and shape, but one is simply located elsewhere in the coordinate plane, then translation would be the correct transformation.
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Reflection: This transformation flips the figure over a line (the line of reflection). If A'B'C' is a mirror image of ABC, then reflection is the transformation.
To identify the exact transformation, you will need to consider the position, size, and orientation of the triangles in question. If you can provide more information about the triangles (like their coordinates or positions), I can assist you further in determining the correct transformation.