Question

l is the midpoint of \\(\overline{km}\\). if \\(lm = 8x\\) and \\(km = 9x + 7\\), what is \\(lm\\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( L \) is the midpoint of \( \overline{KM} \), \( KM = 2 \times LM \). Given \( LM = 8x \) and \( KM = 9x + 7 \), we substitute into the equation:
\( 9x + 7 = 2(8x) \)

Step2: Solve for \( x \)

Simplify the right - hand side: \( 9x + 7 = 16x \)
Subtract \( 9x \) from both sides: \( 7 = 16x - 9x \)
\( 7 = 7x \)
Divide both sides by 7: \( x=\frac{7}{7}=1 \)

Step3: Find \( LM \)

Since \( LM = 8x \) and \( x = 1 \), substitute \( x = 1 \) into the expression for \( LM \):
\( LM=8\times1 = 8 \)

Answer:

\( 8 \)