7. Draw the dilation of ADEF by a scale factor - withcenter of dilation at (0, 0). Then, determine the ratioof the perimeter of the dilated to the original and mLD' ifmLE = 18.5° and m2F = 135°.-5-Ratio of perimeters:D(1,2)E(4, 1)mLD'=F(2, 1)x+5 if it has been dilated by a factor of 4 with

Answered: 7. Draw the dilation of ADEF by a scale…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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7. Draw the dilation of ADEF by a scale factor - with
center of dilation at (0, 0). Then, determine the ratio
of the perimeter of the dilated to the original and mLD' if
mLE = 18.5° and m2F = 135°.
-5-
Ratio of perimeters:
D(1,2)
E(4, 1)
mLD'=
F(2, 1)
x+5 if it has been dilated by a factor of 4 with

Expert Solution

Step 1

If a triangle is dilated by a scale factor k with the center of dilation at the origin, i.e., (0,0), then the dilation is given by

$(x, y) \to (k x, k y)$

$\frac{Perimeter of the dialated figure}{Perimeter of the original figure} = \frac{side of the dialated figure}{Corresponding side of the original figure} = k$ ...(i)

The dilated figure is similar to the original figure.

We know that the corresponding angles of similar figures are congruent.

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

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