The operations on geometric shapes that involves moving, flipping, change of shape, reflection and new shape creation through operations on another shape is known as transformations
- The coordinates of the vertices of the image ΔX'Y'Z' after the composite transformation T₍₋₂, ₄₎ [tex]\circ[/tex] R₀ 180° are X'(-4, -1), Y'(-5, 2), and Z'(-6, 1)
The reason the above values are correct is as follows:
The given transformation sequence is T₍₋₂, ₄₎ [tex]\circ[/tex] R₀ 180°
Where;
T₍₋₂, ₄₎ = A translation two (2) units to the left and four (4) units upwards
R₀ 180° = A rotation of 180° about the origin
The image and preimage of a 180° rotation transformation about the origin is as follows;
Preimage (x, y) [tex]\underset \longrightarrow {R_o \ 180 ^{\circ} }[/tex]Image(-x, -y)
It is to be noted that the first transformation to be performed in a composite transformation is the transformation to the right
The composite transformation is therefore presented as follows;
Combined; (x, y) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] (-x - 2, -y + 4 )
The coordinates of the vertices points on triangle ΔXYZ are X(2, 5), Y(3, 2), Z(4, 3)
Therefore;
The coordinates of the vertices points on triangle ΔX'Y'Z' after the composite transformations are;
- X(2, 5) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] (-2 - 2, -5 + 4 ) = X'(-4, -1)
- Y(3, 2) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] (-3 - 2, -2 + 4 ) = Y'(-5, 2)
- Z(4, 3) [tex]\underset \longrightarrow {T_{-2, \ 4} \circ R_o \ 180 ^{\circ} }[/tex] Z(-4 - 2, -3 + 4 ) = Z'(-6, 1)
Which gives that the coordinates of the triangle ΔX'Y'Z' after the transformation, T₍₋₂, ₄₎ [tex]\circ[/tex] R₀ 180° are;
X'(-4, -1), Y'(-5, 2), and Z'(-6, 1)
Learn more about composite transformations here:
https://brainly.com/question/12907047
