Answer:
Option D is correct
A reflection across y = x , then a translation of 2 units right and 4 units up
Step-by-step explanation:
In triangle ABC
The coordinates are:
A = (0,3) , B =(-2 , 6) and C = (2 , 6)
First do reflection across y =x :
The rule of reflection across y=x is: [tex](x , y) \rightarrow (y , x)[/tex]
then;
[tex](0 , 3) \rightarrow (3 , 0)[/tex]
[tex](-2, 6) \rightarrow (6 , -2)[/tex]
[tex](2, 6) \rightarrow (6 , 2)[/tex]
Now, apply translation of 2 units right and 4 units up.
The rule of translation: [tex](x, y) \rightarrow (x+2 , y+4)[/tex]
[tex](3, 0) \rightarrow (3+2 , 0+4)[/tex] =D (5, 4)
[tex](6, -2) \rightarrow (6+2 , -2+4)[/tex] = F(8, 2) and
[tex](6, 2) \rightarrow (6+2 , 2+4)[/tex] =E(8, 6)
therefore, a reflection across y = x , then a translation of 2 units right and 4 units up prove the △ABC≅△DEF
