The image below shows two dilated figures with lines uv and wx drawn. if the larger figure was dilated using a scale factor of 4, what relationship do lines uv and wx have?

Step-by-step explanation:

The image shows two figures (the larger figure is the image of the smaller figure after dilation).

Lines WX and UV cut two triangles from dilated figures. If the larger figure was dilated using a scale factor of 4, then the larger triangle was dilated using a scale factor of 4 too.

This means that

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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