Question

triangle ABC reflected in the y axes so that the image of triangle ABC is triangle A^ prime B^ prime C . Which of the following statements are true about any reflection ?​

Answer 1

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,

$AB'=\sqrt{(-c-a)^2+(d-b)^2}$

$BA'=\sqrt{(-a-c)^2+(b-d)^2}=\sqrt{(-c-a)^2+(d-b)^2}=AB'$

So, $AB'=BA'$

We know that reflection is rigid transformation, it means figure and its image must be congruent.

$\angle B=\angle B'$

$\triangle ABC\cong \triangle A'B'C'$

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.