Question

△rst is reflected across the line x = 2 to create △rst. what are the coordinates of s?
options: (-3, -1), (-5, -3), (-1, -3), (5, 3), (5, 7)

Explanation:

Step1: Find original coordinates of S

From the graph, original \( S \) has coordinates \( (5, -3) \).

Step2: Apply reflection over \( x = 2 \)

The formula for reflecting a point \( (x, y) \) over the vertical line \( x = a \) is \( (2a - x, y) \). Here, \( a = 2 \), \( x = 5 \), \( y = -3 \).
Calculate new \( x \)-coordinate: \( 2(2) - 5 = 4 - 5 = -1 \).
\( y \)-coordinate remains \( -3 \). So \( S' \) is \( (-1, -3) \).

Answer:

\((-1, -3)\) (corresponding to the option \((-1, -3)\))