Question

Consider the figure above. Starting with the shape in the upper left, identify the figure that has been: -Translated only. -Rotated and translated. -Reflected about the x-axis.

Answer 1

Answers:

Figure a has been translated only (translated 9 units to the right)

Figure b has been reflected over the x axis

Figure c has been rotated and translated

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Explanation:

Pick on a point like (-7,4) and note how it moves 9 units to the right to get to (2,4). All points on the upper left figure follow this same translation rule. This rules in figure a.

Figure b is a result of reflecting over the x axis. The rule used is $(x,y) \to (x,-y)$. The x coordinate stays the same while the y coordinate flips from positive to negative. So for example, (-7,4) flips to (-7,-4)

Figure c is a combination of rotating and translating the original figure. It looks like a 90 counterclockwise rotation has been applied followed by a translation. The actual translation and rotation rules used will depend on how you define the center of rotation.