Final answer:
To find the length of line DP, you need to use the fact that P is the midpoint of DE. After setting up the equation 2(DP) = DE and solving for x, you substitute x back into the expression for DP to find that the length of line DP is 14 units.
Step-by-step explanation:
If P is the midpoint of line DE, then DP and PE are equal in length. Given that DP = 3x + 2 and DE = 10x - 12, we can set up the following equation because the midpoint divides the line segment into two equal parts:
2(DP) = DE
2(3x + 2) = 10x - 12
Solving for x gives us:
6x + 4 = 10x - 12
4x = 16
x = 4
Now, we can find the length of DP by substituting x back into the expression for DP:
DP = 3(4) + 2
DP = 12 + 2
DP = 14
Therefore, the length of line DP is 14 units.