Final answer:
The algebraic expression to find segment MN when N is the midpoint of MP is MN = 18z - 3.5. This is obtained by first expressing the full length of MP as 36z - 7 and then dividing by two since N is the midpoint.
Step-by-step explanation:
The question asks us to find a way to represent the length of segment MN algebraically when point O lies on the line between points M and P, with OM = 34z, OP = 36z - 7, and point N being the midpoint of MP. To solve this, we first express MP as the sum of OM and MP. Since N is the midpoint of MP, MN is half of MP.
MP = OM + PM.
Given that OM = 34z and OP (which is the entire length from O to P) is 36z - 7, we can substitute OP for MP, as point P is the endpoint of the line segment MP.
Therefore, MP = OP = 36z - 7.
Since N is the midpoint of MP, MN will be half of the length of MP:
MN = ½ × MP
MN = ½ × (36z - 7)
MN = 18z - ½ × 7
MN = 18z - 3.5
So, the algebraic expression to find the length of segment MN, given that point N is the midpoint, is MN = 18z - 3.5.