Question

which of the following transformations maps cdef onto cdef? translation left 8 units translation left 14 units reflection across the x - axis reflection across the y - axis rotation 90° clockwise around the origin

Explanation:

Step1: Analyze translation

Translation left 8 units: If we consider a point on CDEF, say point D(4, - 4). Translating it left 8 units gives (4 - 8, - 4)=(-4, - 4). Looking at the graph, D' is not at (-4, - 4), so it's not a translation left 8 units.

Step2: Analyze another translation

Translation left 14 units: Consider point D(4, - 4) again. Translating it left 14 units gives (4 - 14, - 4)=(-10, - 4). D' is not at (-10, - 4), so it's not a translation left 14 units.

Step3: Analyze reflection across x - axis

Reflection across x - axis changes (x,y) to (x, - y). For point D(4, - 4), it would be (4,4). D' is not at (4,4), so it's not a reflection across x - axis.

Step4: Analyze reflection across y - axis

Reflection across y - axis changes (x,y) to (-x,y). For point D(4, - 4), it gives (-4, - 4). For point E(6, - 2), it gives (-6, - 2). For point C(5, - 9), it gives (-5, - 9). For point F(8, - 8), it gives (-8, - 8). These match the coordinates of D', E', C', F' respectively.

Step5: Analyze rotation

Rotation 90° clockwise around the origin changes (x,y) to (y, - x). For point D(4, - 4), it gives (-4, - 4). But the orientation and other points don't match after rotation, so it's not a 90° clockwise rotation.

Answer:

reflection across the y - axis