Respuesta :
The dimensions of the image are twice the dimensions of the preimage,
which indicates that the transformation is a dilation.
- The transformation T is; a dilation transformation with a scale factor of 2, D₂
Reasons:
The transformation applied to ΔABC = T
The image of ΔABC following the transformation, T = ΔA'B'C'
The perimeter of ΔA'B'C' = Twice the perimeter of ΔABC
Therefore, we have;
A'B' + B'C' + A'C' = 2 × (AB + BC + AC)
Which gives
A'B' + B'C' + A'C' = 2·AB + 2·BC + 2·AC
By similar triangles, we have the ratio of corresponding sides as follows;
[tex]\displaystyle \frac{AB}{A'B'} = \frac{BC}{B'C'} = \mathbf{ \frac{AC}{A'C'}}[/tex]
Which gives;
[tex]\displaystyle \frac{AB}{A'B'} = \frac{AB}{2 \cdot AB} = \frac{1}{2}[/tex]
A'B' = 2·AB
Therefore;
- Triangle ΔA'B'C' is twice the dimension of triangle ΔABC, and T is a dilation transformation with a scale factor of 2, D₂
Learn more about dilation transformation here:
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