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

Option D.

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'=√((-c-a)^2+(d-b)^2)`

`BA'=√((-a-c)^2+(b-d)^2)=√((-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.