Final answer:
In triangle ABC, point M is the midpoint of AC and point D lies on BM such that MD and DB are in the ratio 1:4. Therefore, the answers to the given options are: a) MD:BD = 1:4, b) AD:DC = 1:4, c) DM:MB = 1:1, and d) AM:MC = 1:1.
Step-by-step explanation:
In triangle ABC, point M is the midpoint of AC, and point D lies on BM such that MD and DB are in the ratio 1:4.
a) To find the length of MD and DB, let's suppose that MD is equal to x. Since MD and DB are in the ratio 1:4, the length of DB is 4x.
b) To find the ratio of AD and DC, we can use the fact that M is the midpoint of AC. This means that AM is equal to MC. Since MD is 1/5 of BM, we can conclude that AD is 1/5 of AB and DC is 4/5 of AB. Therefore, AD:DC = 1:4.
c) Since M is the midpoint of AC, we know that AM is equal to MC.
d) Since M is the midpoint of AC, we know that AM is equal to MC.