The only transformation that can lead triangle ABC to triangle A”B”C” is a translation followed by a rotation.
Let's analyze each option:
a) reflection followed by a rotation
A reflection flips a figure across a line, while a rotation turns a figure around a fixed point. If we perform a reflection followed by a rotation on triangle ABC, the resulting triangle will not be the same as triangle A”B”C”. This is because a reflection cannot change the orientation of a triangle, and a rotation alone cannot change the position of a triangle.
b) translation followed by a rotation
A translation moves a figure along a straight line, while a rotation turns a figure around a fixed point. If we perform a translation followed by a rotation on triangle ABC, we can obtain triangle A”B”C”. The translation will move triangle ABC to the same position as triangle A’B’C’, and the rotation will then rotate triangle A’B’C’ to the position of triangle A”B”C”.
c) translation followed by a reflection
A translation moves a figure along a straight line, while a reflection flips a figure across a line. If we perform a translation followed by a reflection on triangle ABC, we will not obtain triangle A”B”C”. This is because a translation cannot change the orientation of a triangle, and a reflection alone cannot change the position of a triangle.
Therefore, the only transformation that can lead triangle ABC to triangle A”B”C” is a translation followed by a rotation.