Question

determine the transformation:

Explanation:

Step1: Identify Coordinates

First, find the coordinates of the original and transformed points.
Original: \( T(2,1) \), \( S(8,1) \), \( R(8,6) \)
Transformed: \( T'(-2,1) \), \( S'(-8,1) \), \( R'(-8,6) \)

Step2: Analyze X - Coordinate Change

For each point, the \( x \)-coordinate changes as \( x \to -x \) (e.g., \( T(2,1) \to T'(-2,1) \), \( S(8,1) \to S'(-8,1) \), \( R(8,6) \to R'(-8,6) \)). The \( y \)-coordinate remains the same.

Step3: Determine Transformation

A transformation where \( (x,y) \to (-x,y) \) is a reflection over the \( y \)-axis.

Answer:

The transformation is a reflection over the \( y \)-axis (or a horizontal reflection, \( (x, y) \to (-x, y) \)).