Final answer:
The correct length of segment AD is 10 units because point M is the midpoint of AB, AC equals CM, and MD equals DB with MD given as 5 units. Using these properties, we determined the entire length of AD by adding AC and CD, which are both equal to 5 units. The correct option for the length of AD is (c) 10 units.
Step-by-step explanation:
Solving the Mathematical Problem
To find the length of AD when point M is the midpoint of AB, and points C and D are on AB in such a way that AC = CM and MD = DB, and given MD = 5, we use the property of midpoints and segments.
Given that M is the midpoint of AB, AM = MB. Since AC = CM, then AC = AM. Similarly, as MD = DB, MD = MB. We are given that MD (which is also MB) is 5 units in length.
The length of AD is the sum of AC (which is equal to AM) and CD. Because MD and DB are the same, and MD is given as 5, then the entire length of AB is twice the length of MD, which is 2 × 5 = 10 units. The length of AC is half of AB since M is the midpoint, so AC is 5 units.
Therefore, the length of AD, which is AC plus CD (CD being equivalent to MD), is 5 + 5 = 10 units.
The correct option for the length of AD is (c) 10 units.