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Lorico [155]
3 years ago
11

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]3 years ago
5 0

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.

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\\(i)\\&#10;\text{We know that the average rate of change of a function f(x) on inerval [a,b] is}\\&#10;\\&#10;f_{avg}=\frac{f(b)-f(a)}{b-a}\\&#10;\\&#10;\text{so using this the average rate of chang of g for x on interval }[3,7] \text{ is}\\&#10;\\&#10;g_{avg}=\frac{g(7)-g(3)}{7-3}\\&#10;\\&#10;=\frac{4-1}{4}\\&#10;\\&#10;=\frac{3}{4}\\&#10;\\&#10;\text{so average rate of change of g on interval [3,7] is }\frac{3}{4}

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