Math Problem Statement
Point V is on line segment start overline, U, W, end overlineUW. Given U, V, equals, 6, commaUV=6, U, W, equals, 5, x, commaUW=5x, and V, W, equals, 4, x, minus, 1, commaVW=4x−1, determine the numerical length of start overline, V, W, end overline, .VW.
Solution
We are given that point is on line segment , with the following information:
- ,
- ,
- .
Since is on the line segment , we know that:
Substitute the given values into this equation:
Now, simplify and solve for :
Now that we have , substitute this back into the expression for :
Thus, the numerical length of is .
Would you like more details or have any questions? Here are 5 related questions you could explore:
- How would you solve for if were unknown?
- What is the length of the entire line segment ?
- If were not on the line segment , how would that affect the solution?
- How would the equation change if were a function of ?
- Can you express the position of on as a fraction of ?
Tip: When solving for unknowns in geometry problems, always write down known relationships, such as segment addition postulates, to simplify the solution!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Geometry
Segment Addition Postulate
Formulas
UV + VW = UW
Theorems
Segment Addition Postulate
Suitable Grade Level
Grades 8-10