Question

what single transformation maps \\(\delta abc\\) onto \\(\delta abc\\)?

rotation \\(90^\circ\\) clockwise about the origin
rotation \\(90^\circ\\) counterclockwise about the origin
reflection across the x-axis
reflection across the line \\(y = x\\)

Explanation:

Identify the coordinates of the original vertices

Using the Geometric Transformations knowledge point

$$ A = (-3, 1), \quad B = (-1, 2), \quad C = (-2, 1) $$

Identify the coordinates of the image vertices

Using the Geometric Transformations knowledge point

$$ A' = (-1, -3), \quad B' = (-2, -1), \quad C' = (-1, -2) $$

Determine the coordinate mapping rule

Using the Rotations in the Coordinate Plane knowledge point

$$
LATEXBLOCK0
$$

Match the rule to a standard transformation

Using the Rotations in the Coordinate Plane knowledge point

$$ (x, y) ightarrow (y, -x) \iff \text{rotation } 90^\circ \text{ clockwise about the origin} $$

Answer:

• rotation 90° clockwise about the origin (Correct answer)
• rotation 90° counterclockwise about the origin
• reflection across the x-axis
• reflection across the line y = x