Answer:
Step-by-step explanation:
Given rule for the multiple translations is,
[tex]T_{5,-0.5}.R_{0.180^{\circ}}(x,y)[/tex]
Apply the rule [tex]R_{0,180^{\circ}}[/tex] first.
(x, y) → (-x, -y)
This rule illustrates a rotation of the triangle FGH by 180° about the origin,
Vertices of ΔFGH are,
F → (1, 1)
G → (4, 5)
H → (5, 1)
After rotation vertices of the image triangle are,
F' → (-1, -1)
G' → (-4, -5)
H' → (-5, -1)
Further apply the rule,
[tex]T_{5,-0.5}[/tex]
(x, y) → (x + 5, y - 0.5)
By this rule of translation,
F'(-1, -1) → F"{(-1 + 5), (-1 - 0.5)}
→ F"(4, -1.5)
G'(-4, -5) → G"[(-4 + 5), (-5 - 0.5)]
→ G"(1, -5.5)
H'(-5, -1) → H"[(-5 + 5), (-1 -0.5)]
→ H"(0, -1.5)
