Question

Which glide reflection describes the mapping ABC DEF

Answer 1

As you can see in the figure attached, the vertex E is shifted 6 units down from the vertex B and it has the coordinates (1,-1).  
 If you draw the line x=-1 you will notice that the vertex B is 2 units left from the line and the vertex E is 2 units rigtht from the line.
 So, if you shifted the triangle ABC 6 units down and then you reflect it across x=-1, you will obtain the triangle DEF.
 Therefore, as you can see, the answer for the exercise shown above is:
 (x, y) (x, y-6) and reflected across x=-1

Answer 2

Answer:

Option D is correct.

$(x, y) \rightarrow (x, y-6)$ and reflected across x = -1

Step-by-step explanation:

From the given figure:

The coordinates of ABC are:

A(-7, 2), B(-3, 5) and C(-3, 1)

first apply the rule of translation on ABC i.e:

$(x, y) \rightarrow (x, y-6)$

Then;

$A(-7, 2) \rightarrow (-7, 2-6)=(-7, -4)$

$B(-3, 5) \rightarrow (-3, 5-6)=(-3, -1)$

$B(-3, 1) \rightarrow (-3, 1-6)=(-3, -5)$

Next, reflect it across x = -1

The rule of reflection across x = -1 i.,e

$(x, y) \rightarrow (-(x+1)-1, y)$

or

$(x, y) \rightarrow (-x-2, y)$

then;

$(-7, -4) \rightarrow (7-2, -4)=(5, -4)=D$

$(-3, -1) \rightarrow (3-2, -1)=(1, -1)=E$

$(-3, -5) \rightarrow (3-2, -5)=(1, -5)=F$

Therefore, the glide reflection describes the mapping ABC to DEF  is:

$(x, y) \rightarrow (x, y-6)$ and reflected across x = -1