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Given the preimage and image,find the dilation scale factor.​

Given the preimage and image,find the dilation scale factor.​-example-1
User Alturkovic
by
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1 Answer

2 votes

Answer:

The dilation scale factor is
(1)/(2).

Explanation:

The image is the dilated form of its preimage if and only if the following conditions are observed:

1)
K' = \alpha_(1) \cdot K

2)
T' = \alpha_(2) \cdot T

3)
P' = \alpha_(3) \cdot P

4)
J' = \alpha_(4) \cdot J

5)
\alpha_(1) = \alpha_(2) = \alpha_(3) = \alpha_(4)

If we know that
K = (2, 0),
K' = (1, 0),
T = (3, 0),
T' = (1.5,0),
P = (1, 5),
P' = (0.5, 2.5),
J = (0, 3) and
J' = (0, 1.5), then the coefficients are, respectively:


\alpha_(1) = (1)/(2),
\alpha_(2) = (1)/(2),
\alpha_(3) = (1)/(2),
\alpha_(4) = (1)/(2)

As
\alpha_(1) = \alpha_(2) = \alpha_(3) = \alpha_(4), we conclude that the dilation scale factor applied in the preimage is equal to
(1)/(2).

User ShadSterling
by
7.3k points

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