A similarity transformation maps `Delta`ABC to `Delta`JKL. The measure of `/_A` of preimage `Delta`ABC is 105°. The scale factor

Question

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A similarity transformation maps `Delta`ABC to `Delta`JKL. The measure of `/_A` of preimage `Delta`ABC is 105°. The scale factor

of the dilation in the similarity transformation is 1.5. If `/_A` in the preimage corresponds to `/_J` in the image, what is m`/_J`?

Mathematics

1 answer:

RoseWind [281] · Answer 1 · 2021-12-07T15:05:30+03:00

Please note that dilation does not affect angles. Thus, if an image is dilated the angle remains the same and does not change.

Therefore, even if $\Delta ABC$ is dilated to $\Delta JKL$ by a factor of 1.5 (or by any factor for that matter), the linear dimensions of the original triangle $\Delta ABC$ will either get stretched or get shrunk by a factor of 1.5 but the angles of the original triangle will not be affected in any case.

Please note that this is true for all two dimensional geometric shapes.