Given triangle $f$ on the coordinate grid, which triangle represents a translation of triangle $f$?

• A. A triangle that is rotated $90°$ about the origin from $f$
• B. A triangle that is a mirror image of $f$ across the y-axis
• C. A triangle that is congruent to $f$ and located in a different position without rotation or reflection
• D. A triangle that is twice as large as $f$ but in the same position

Answer: (C)

Verified step by step guidance

1. Recall the definition of a translation in geometry: a translation moves every point of a figure the same distance in the same direction, resulting in a figure congruent to the original but in a different position without any rotation or reflection.
2. Analyze the options given: a 90° rotation about the origin changes the orientation of the triangle, so it is not a translation.
3. A mirror image across the y-axis is a reflection, which changes the orientation and is not a translation.
4. A triangle that is twice as large is a dilation (scaling), not a translation, because the size changes.
5. Therefore, the correct representation of a translation is a triangle congruent to the original and located in a different position without rotation or reflection.