Question

What series of transformations map △ABC onto ​ △DEF ​ to prove that △ABC≅△DEF ?



a reflection across y-axis then translation of 3 units right and 5 units up

a clockwise rotation of 180° about the origin then a translation 3 units right and 1 unit up

a reflection across y-axis then translation of 1 unit right and 1 unit down

a reflection across y = x then a translation of 2 units right and 4 units up

Answer 1

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: $(x , y) \rightarrow (y , x)$

then;

$(0 , 3) \rightarrow (3 , 0)$

$(-2, 6) \rightarrow (6 , -2)$

$(2, 6) \rightarrow (6 , 2)$

Now, apply translation of 2 units right and 4 units up.

The rule of translation: $(x, y) \rightarrow (x+2 , y+4)$

$(3, 0) \rightarrow (3+2 , 0+4)$ =D (5, 4)

$(6, -2) \rightarrow (6+2 , -2+4)$ = F(8, 2)   and

$(6, 2) \rightarrow (6+2 , 2+4)$ =E(8, 6)  

therefore, a reflection across y = x , then a translation of 2 units right and 4 units up prove the △ABC≅△DEF

Answer 2

Answer:

a reflection across y = x then a translation of 2 units right and 4 units up

Step-by-step explanation: