Math Problem Statement

Point O is on line segment start overline, N, P, end overline NP . Given O, P, equals, 2OP=2 and N, O, equals, 17, commaNO=17, determine the length start overline, N, P, end overline, . NP .

Solution

Let's solve the problem step-by-step to find the length of NP\overline{NP}.

Given:

  1. Point OO is on the line segment NP\overline{NP}.
  2. OP=2OP = 2
  3. NO=17NO = 17

To Find:

The length of NP\overline{NP}.

Solution:

Since point OO is on the line segment NP\overline{NP}, we can say:

NP=NO+OPNP = NO + OP

Now, substitute the given values:

NP=17+2NP = 17 + 2

NP=19NP = 19

Conclusion:

The length of NP\overline{NP} is 19\boxed{19}.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

  1. What is the midpoint of a line segment, and how is it calculated?
  2. How do you find the length of a line segment when given coordinates of its endpoints?
  3. How can you determine if three points are collinear?
  4. What is the distance formula in a coordinate plane?
  5. How is the section formula used to divide a line segment in a given ratio?

Tip: When solving geometry problems, always visualize the problem with a diagram to understand the relationships between points and lines.

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Math Problem Analysis

Mathematical Concepts

Geometry
Line Segments
Addition of Segment Lengths

Formulas

Length of line segment: NP = NO + OP

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 6-8