Triangle ABC transformation to A'B'C' is given by, a [tex]180[/tex]° rotation about the origin and then a translation [tex]3[/tex] units up and [tex]1[/tex]unit left.
What is transformation?
" Transformation is defined as the change in two dimensional geometrical shape in the coordinate plane by the process of reflection, rotation, and translation."
According to the question,
Given,
On a coordinate plane triangle ABC with points,
[tex]A(-4,-1) , B(-5,-5), C(-3,-4)[/tex]
After transformation new points of A'B'C' are
[tex]A(3,4) , B( 4,8) , C(2,7)[/tex]
- When [tex]A(-4,-1)[/tex]rotate [tex]180[/tex] degrees about the origin it reaches to [tex](4,1)[/tex] translation [tex]3[/tex] units up change its y- coordinate and [tex]1[/tex] unit left change in x- coordinate. After transformation coordinate of its image is given by
[tex]A' ( 4-1, 1+3) = A' (3,4)[/tex]
- When [tex]B(-5,-5)[/tex]rotate [tex]180[/tex] degrees about the origin it reaches to [tex](5,5)[/tex] translation [tex]3[/tex] units up change its y- coordinate and [tex]1[/tex] unit left change in x- coordinate.After transformation coordinate of its image is given by
- [tex]B' ( 5-1, 5+3) = B' (4,8)[/tex]
- When [tex]C(-3,-4)[/tex]rotate [tex]180[/tex] degrees about the origin it reaches to [tex](3,4)[/tex] translation [tex]3[/tex] units up change its y- coordinate and [tex]1[/tex] unit left change in x- coordinate.After transformation coordinate of its image is given by
- [tex]C' ( 3-1, 4+3) = C' (2,7)[/tex]
Hence, triangle ABC transformation to A'B'C' is given by, a [tex]180[/tex]° rotation about the origin and then a translation [tex]3[/tex] units up and [tex]1[/tex]unit left.
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