Video: Understanding the Effect of Rotation on a Given Figure

Which of the following represents a rotation of the shaded figure? [A] Figure A [B] Figure B [C] Figure C [D] Figure D

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Video Transcript

Which of the following represents a rotation of the shaded figure?

Let’s begin by recalling that a rotation is the transformation that turns a shape in a circular motion about a point. If you find it difficult to visualize transformations or even rotations, it can be helpful to use tracing paper. Put the tracing paper over the shape and trace over the outline. As we’re thinking about a rotation, it can be helpful to put our pencil point anywhere on the tracing paper and turn it and then see what happens. Out of the options that we’re given, the option (C) produces a rotation.

Just like in the sketch, if we placed our pencil point with the tracing paper here and rotated the shaded figure 90 degrees clockwise, then we’d end up with the following image. We could’ve also rotated 270 degrees counterclockwise and achieved the same image. Therefore, option (C) is the correct answer. But let’s have a quick look at the other options.

Option (A) has two shapes which look like a mirror image of each other. Therefore, this is a reflection. The line of reflection would appear halfway between these two shapes. But it’s not a rotation, so it’s not the answer. In option (B), the image is four places to the right of the original shaded figure, indicating that this is a translation but not a rotation. In option (D), this shaded figure and the unshaded figure are not congruent or similar. Therefore, this doesn’t represent any transformation and certainly not a rotation. So, we can give the answer as option (C).

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