Final answer:
To find the length of line segment CD when D is the midpoint of CF, we set up an equation 2CD = CF, using the given expressions for CF and CD. After simplifying the equation and solving for y, we substitute the value back into the expression for CD and determine that CD is 4 cm long.
Step-by-step explanation:
The student has asked to find the length of the line segment CD given that D is the midpoint of CF, and they have provided the lengths of the line segments CF and CD in terms of y. Because D is the midpoint, we know that CD is equal to DF. Therefore, we can set up the problem as an equation where 2CD equals CF. Using the given lengths, we have:
2CD = 2y - 2
Then, we incorporate the length of CD given in the problem as CD = 3y - 11 into the equation:
2(3y - 11) = 2y - 2
After expanding and simplifying the equation, we obtain:
6y - 22 = 2y - 2
Now, we solve for y:
6y - 2y = 22 - 2
4y = 20
y = 5
Substituting y back into the length of CD:
CD = 3(5) - 11
CD = 15 - 11
CD = 4 cm
Hence, the length of the line segment CD is 4 cm.