Question

clayton needs to reflect the triangle below across the line \\(y = x\\).

Explanation:

Identify the coordinates of the vertices

Using the Coordinate Transformations knowledge point, we read the coordinates of the vertices of triangle \(ABC\) from the given coordinate grid:

$$ A = (5, 7),\quad B = (6, 2),\quad C = (4, 4) $$

Apply the reflection rule

Using the Reflection Across Line y=x knowledge point

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

Calculate the reflected coordinates

Using the Reflection Across Line y=x knowledge point

$$
LATEXBLOCK0
$$

Answer:

The coordinates of the reflected triangle \(A'B'C'\) are:

$$ A' = (7, 5),\quad B' = (2, 6),\quad C' = (4, 4) $$