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 ?

Question

asked Jan 22, 2021 107k views

1 Answer

Martin Sznapka · Answer 1 · 2021-01-28T21:51:42+0000

Answer:

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.