Triangle 𝐵𝐸𝐹 is the image of triangle 𝐵𝐷𝐹 by reflection across what.
To start, let’s think what possible thing we could be writing for our missing value. Is it, for example, a shape or a line or a point? Well, let’s recall that if we wanted to describe a reflection, we would first need to state what object is being reflected. And then, we would need to say the line of reflection.
In our question, triangle 𝐵𝐷𝐹 is the object that’s being reflected. And therefore, our missing word or description must be the line of reflection. So we’re told that triangle 𝐵𝐸𝐹 is the image of triangle 𝐵𝐷𝐹. We can see that point 𝐸 is a reflection of point 𝐷. And we can see that point 𝐹 is the image of itself, and point 𝐵 is also the image of itself.
This means that both these two points must lie on the line of reflection. Therefore, our line of reflection is the line 𝐹𝐵. So we have triangle 𝐵𝐸𝐹 is the image of triangle 𝐵𝐷𝐹 by reflection across the line 𝐹𝐵.