If triangle def is translated 5 units down, what will be the coordinates of point e ′ in the image?

 The correct option is

(B) (4, -2).

Step-by-step explanation:  Given that the triangle DEF is translated  units down.

We are to find the co-ordinates of point E' in the image.

From the graph, we note that

the co-ordinates of the vertices of triangle DEF are D(1, 2), E(4, 3) and F(3, 1).

We know that

if a point (x, y) is translated 5 units down, then its co-ordinates becomes

(x, y)  →  (x, y-5).

Therefore, after translation, the co-ordinates of the vertex E' in the image are

E(4, 3)  →   E'(4, 3-5) = E'(4, -2).

Thus, (B) is the correct option.