If G is the midpoint of FH, find FG.
Understand the Problem
The question is asking us to find the length of segment FG given that point G is the midpoint of segment FH, where the positions of points F and H are expressed as algebraic expressions in terms of x. This problem involves calculating FG using the midpoint formula.
Answer
The length of segment FG is $-4x + 8$.
Answer for screen readers
The length of segment FG is $-4x + 8$.
Steps to Solve
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Identify the positions of points F and H
The position of point F is given as $11x - 7$ and the position of point H is $3x + 9$. -
Use the midpoint formula
The midpoint formula states that the midpoint $G$ of segment $FH$ can be calculated using the formula: $$ G = \frac{F + H}{2} $$ -
Substitute the expressions for F and H into the midpoint formula
Now, substituting the expressions for F and H: $$ G = \frac{(11x - 7) + (3x + 9)}{2} $$ -
Simplify the expression for G
Combine like terms in the numerator: $$ G = \frac{(11x + 3x) + (-7 + 9)}{2} = \frac{14x + 2}{2} $$
Then simplify: $$ G = 7x + 1 $$ -
Calculate the length of FG
To find the length of segment $FG$, we can use the formula: $$ FG = G - F $$ Substituting for G and F: $$ FG = (7x + 1) - (11x - 7) $$ -
Simplify the expression for FG
This simplifies to: $$ FG = 7x + 1 - 11x + 7 = -4x + 8 $$
The length of segment FG is $-4x + 8$.
More Information
The length of segment FG is expressed in terms of x. As x changes, the length of FG will also change. If x is defined within a certain range, one can calculate specific lengths.
Tips
- Forgetting to distribute the negative sign when subtracting the position of F from G.
- Not simplifying fully after subtraction, which could lead to an incorrect result.
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