Question

what is the pre-image of vertex a if the image shown on the graph was created by a reflection across the line \\(y = x\\)?

\\((10, -2)\\)
\\((-10, 2)\\)
\\((-2, -10)\\)
\\((2, 10)\\)

Explanation:

Identify the coordinates of vertex \(A'\)

From the given coordinate grid, locate the vertex \(A'\):

$$ A' = (-2, 10) $$

Apply the inverse reflection rule

The image was created by a reflection across the line \(y = x\). The coordinate rule for a reflection across \(y = x\) is:

$$ (x, y) ightarrow (y, x) $$

To find the pre-image \(A\) from the image \(A'(x', y')\), we apply the inverse transformation:

$$ (x, y) = (y', x') $$

Calculate the pre-image coordinates

Substitute the coordinates of \(A'(-2, 10)\) into the inverse rule:

$$ A = (10, -2) $$

Answer:

• (A) \((10, -2)\) (Correct answer)
• (B) \((-10, 2)\)
• (C) \((-2, -10)\)
• (D) \((2, 10)\)