Subtitles section Play video
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- [Instructor] We are told, Brenda was able to map
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circle M onto circle N
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using a translation and a dilation.
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This is circle M right over here.
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Here's the center of it.
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This is circle M, this circle right over here.
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It looks like at first, she translates it.
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The center goes from this point to this point here.
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After the translation, we have the circle
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right over here.
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Then she dilates it.
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The center of dilation looks like it is point N.
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She dilates it with some type of a scale factor
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in order to map it exactly onto N.
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That all seems right.
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Brenda concluded, "I was able to map circle M
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"onto circle N using a sequence
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"of rigid transformations,
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"so the figures are congruent."
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Is she correct?
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Pause this video and think about that.
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Let's work on this together.
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She was able to map circle M onto circle N
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using a sequence of transformations.
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She did a translation and then a dilation.
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Those are all transformations,
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but they are not all rigid transformations.
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I'll put a question mark right over there.
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A translation is a rigid transformation.
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Remember, rigid transformations are ones
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that preserve distances,
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preserve angle measures, preserve lengths,
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while a dilation is not a rigid transformation.
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As you can see very clearly,
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it is not preserving lengths.
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It is not, for example, preserving the radius
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of the circle.
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In order for two figures to be congruent,
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the mapping has to be only with rigid transformations.
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Because she used a dilation,
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in fact, you have to use a dilation
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if you wanna be able to map M onto N
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because they have different radii,
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then she's not correct.
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These are not congruent figures.
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She cannot make this conclusion.
