Applying the segment addition theorem, the length of NP = 30 units.
How to Apply the Segment Addition Theorem?
Since we are given that point O lies on line segment NP, it means that points O, N, and P are collinear. By implication, we would have the following equation based on the segment addition theorem:
NO + OP = NP.
Given the following:
NP = 4x + 10
NO = 4x
OP = x + 5
Substitute the values into the NO + OP = NP:
4x + x + 5 = 4x + 10
5x + 5 = 4x + 10
Combine like terms
5x - 4x = -5 + 10
x = 5
Length of NP = 4x + 10
Plug in the value of x
Length of NP = 4(5) + 10
Length of NP = 20 + 10
Length of NP = 30 units
Thus, applying the segment addition theorem, the length of NP = 30 units.
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