In which line must triangle 𝐹𝐷𝐿 be reflected to map it onto triangle 𝐹𝐶𝐿?
Let’s start by highlighting triangle 𝐹𝐷𝐿 and triangle 𝐹𝐶𝐿. Here’s triangle 𝐹𝐷𝐿. And here’s triangle 𝐹𝐶𝐿. In a reflection, every point is the same distance from the central line. And the central line is the line that is being reflected over.
Our points 𝐹 and 𝐿 are not changing. Point 𝐷 turns into point 𝐶. Point 𝐷 and point 𝐶 are the same distance from the line 𝐹𝐸. 𝐶 is four units away from the line 𝐹𝐸. And 𝐷 is four units away from the line 𝐹𝐸. Because points 𝐹 and 𝐿 lie on the central line, they won’t change.
Triangle 𝐹𝐷𝐿 can be reflected over line 𝐹𝐸 to produce triangle 𝐹𝐶𝐿.