Math Problem Statement
If B is the midpoint of AC, and AC = 8x - 20, find BC. AB = 3x - 1.
Solution
In this problem, we are given the following information:
- is the midpoint of .
- .
- .
- We are asked to find .
Step-by-Step Solution
Since is the midpoint of , it divides the line segment into two equal parts. This means:
Also, since , we can express as . So:
Substituting the values we know:
Solve for :
Now, simplify:
Find :
Since and , substitute into the expression for : So, .
Final Answer:
Would you like more details or have any further questions?
Here are five related questions for further practice:
- If and , how do you find ?
- What happens to the length of if is no longer the midpoint of ?
- How would the equation change if and were in a ratio of 2:1?
- If was expressed as a quadratic function, how would you solve for the length of ?
- What if was a function of another variable, say ? How would you approach the solution?
Tip: Always check midpoint problems by confirming that , which ensures your equation setup is correct.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Midpoint
Formulas
AC = AB + BC
Since B is the midpoint: AB = BC
Theorems
Midpoint Theorem
Suitable Grade Level
Grades 8-10