Question

identify the single transformation shown in the diagram: *
translation
reflection
dilation
rotation

Explanation:

• Translation: A translation slides a figure without rotating or flipping it. But here, the orientation relative to a vertical line (like the y - axis) changes, so it's not a translation.
• Dilation: A dilation changes the size of a figure. The two triangles (the original and the transformed one) are of the same size, so it's not a dilation.
• Rotation: A rotation turns a figure around a point. But the key property of a reflection is that each point of the original figure has a corresponding point on the transformed figure such that the line of reflection is the perpendicular bisector of the segment joining the two points. Here, if we consider a vertical line (the y - axis in a coordinate - like grid), each point of the purple triangle has a mirror - image point on the black triangle with respect to that vertical line.
• Reflection: A reflection flips a figure over a line. In the given diagram, the black triangle is the mirror - image of the purple triangle across a vertical line (which acts as the line of reflection).

Answer:

Reflection