Answer:
Option D.
Step-by-step explanation:
It is given that triangle ABC reflected in the y axes so that the image of triangle ABC is triangle A'B'C'.
Let A(a,b) and B(c,d). So, after reflection A'(-a,b) and B'(-c,d).
Using distance formula,
[tex]AB'=\sqrt{(-c-a)^2+(d-b)^2}[/tex]
[tex]BA'=\sqrt{(-a-c)^2+(b-d)^2}=\sqrt{(-c-a)^2+(d-b)^2}=AB'[/tex]
So, [tex]AB'=BA'[/tex]
We know that reflection is rigid transformation, it means figure and its image must be congruent.
[tex]\angle B=\angle B'[/tex]
[tex]\triangle ABC\cong \triangle A'B'C'[/tex]
If triangle ABC is read clockwise, then after reflection triangle A'B"C' is read anticlockwise.
Since statements I, II and IV are true, therefore the correct option is D.
