The correct answer is:
B. This is a dilation about (0, 0) with a scale factor of 4; A'(8, 4), B' (16, 4), C' (16, -12).
Step-by-step explanation:
Given
Dilation: D : (x,y) => (4x,4y)
And Vertices
A ( 2, 1 ), B ( 4, 1 ), C ( 4, -3 )
Applying dilation on all vertices
![A ( 2, 1 ) => A'(4*2, 4*1) => A'(8,4)\\B ( 4, 1 ) = > B' (4*4 ,4*1) = > B'(16,4)\\C(4,-3) => C' (4*4 , 4*-3) => C'(16, -12)](https://tex.z-dn.net/?f=A%20%28%202%2C%201%20%29%20%3D%3E%20A%27%284%2A2%2C%204%2A1%29%20%3D%3E%20A%27%288%2C4%29%5C%5CB%20%28%204%2C%201%20%29%20%3D%20%3E%20B%27%20%284%2A4%20%2C4%2A1%29%20%3D%20%3E%20B%27%2816%2C4%29%5C%5CC%284%2C-3%29%20%3D%3E%20C%27%20%284%2A4%20%2C%204%2A-3%29%20%3D%3E%20C%27%2816%2C%20-12%29)
To find the scale factor,
As we are multiplying each vertex coordinate by 4, the dilation factor is 4.
Moreover,
![\frac{A'}{A} = \frac{(8,4)}{(2,1)} = (4,4)](https://tex.z-dn.net/?f=%5Cfrac%7BA%27%7D%7BA%7D%20%3D%20%5Cfrac%7B%288%2C4%29%7D%7B%282%2C1%29%7D%20%3D%20%284%2C4%29)
Hence the scale factor is 4.
So,
The correct answer is:
B. This is a dilation about (0, 0) with a scale factor of 4; A'(8, 4), B' (16, 4), C' (16, -12).
Keywords: Dilation, Scale factor
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