Answer:
750 m
Step-by-step explanation:
Theorem:
In a triangle, a segment whose endpoints are the midpoints of two sides is parallel and half the length of the third side.
In triangle LMN, segment DF has endpoints which are midpoints of sides LM and MN. That makes segment DF parallel to side LN and half the length of LN.
The shortest path from point D to point N is segments DF and FN.
Point F is the midpoint of segment MN.
MN = 800 m
FN = (1/2)MN = (1/2)(800 m) = 400 m
From the theorem,
DF = (1/2)LN
DF = (1/2)(700 m) = 350 m
shortest path = DF + FN = 350 m + 400 m = 750 m
Answer: 750 m
