Question

triangle \\(pqr\\) is reflected across a line, \\(p = (4,-5)\\), and \\(p = (-4, -5)\\). what is the line of reflection?

the x-axis
the y-axis
the line \\(y = x\\)
the line \\(y = -x\\)

Explanation:

Identify the coordinates of the original point and its image

$$ P = (4, -5), \quad P' = (-4, -5) $$

Analyze the coordinate transformation

$$ (x, y) \to (-x, y) $$

Determine the line of reflection

$$ \text{The transformation } (x, y) \to (-x, y) \text{ represents a reflection across the } y\text{-axis.} $$

Answer:

• the x-axis
• the y-axis (Correct answer)
• the line \(y = x\)
• the line \(y = -x\)