The vertices of ∆def are d(2, –4), e(3, –4), and f(3, –2).

which figure shows the image of ∆def for a glide reflection where the translation is (x, y) → (x, y + 5) and the line of reflection is x = 0?

answers are the two graphs in the picture

a: first graph
b: second graph

A: First graph

Step-by-step explanation:

* In the translation

- If we move the figure horizontally, means left or right, we change

 the x-coordinate

# Ex: if point (x , y) translated horizontally a units to the right,

  then its image is (x - a , y), or if it translated horizontally b units

  to the left, then its image is (x + b , y)

- If we move the figure vertically, means up or down, we change

 the y-coordinate

# Ex: if point (x , y) translated vertically c units up,

  then its image is (x , y + c), or if it translated vertically d units

  down, then its image is (x , y - d)

∵ Triangle DEF translated by (x , y) → (x , y + 5), that means

   translate it by 5 units up ⇒ translated vertically

∵ D (2 , -4) , E (3 , -4) and F (3 , -2)

- Add every y-coordinate 5 unites

- (-4) + 5 = 1 , (-4) + 5 = 1 , (-2) + 5 = 3

∴ D' (2 , 1) , E' (3 , 1) and F' (3 , 3)

* The reflection on the line x = 0, means a reflection across the y-axis

 because x = 0 means the points on y-axis

- The reflection across the y-axis change the sign of the

  x-coordinates

∴ D" (-2 , 1) , E" (-3 , 1) and F" (-3 , 3)

* Look to the graph you will find these points on the first

 graph in the second photo

constants mean the stopped points or the points on a graph that nothing is changing, hope this

step-by-step explanation: