Question

which statement about this figure is true?
transformation 1:
rotate the figure 90° around
point a.
transformation 2:
reflect the figure across
line m.
this figure does not have symmetry.
applying transformation 1 twice carries the figure onto
itself.
applying transformation 1 carries the figure onto itself.
applying transformation 2 carries the figure onto itself.

Explanation:

Step1: Analyze symmetry

The figure has a vertical line of symmetry (line \(m\)). So the statement “This figure does not have symmetry” is false.

Step2: Analyze Transformation 1

Transformation 1 is a \(90^{\circ}\) rotation. A \(90^{\circ}\) rotation (Transformation 1) does not carry the figure onto itself. Rotating \(90^{\circ}\) twice (\(180^{\circ}\) rotation) also does not carry the figure onto itself (because of the non - symmetric features like the mouth).

Step3: Analyze Transformation 2

Transformation 2 is a reflection across line \(m\). Since line \(m\) is a line of symmetry of the figure, reflecting (Transformation 2) the figure across line \(m\) carries the figure onto itself.

Answer:

Applying Transformation 2 carries the figure onto itself.