Question

9 use the diagram to answer the question below. suppose ( jm = 48x + 25 ) and ( mk = 43x + 35 ) if ( m ) is the midpoint of ( overline{jk} ), what is ( overline{mk} )? ( mk = square )

Explanation:

Step1: Set JM equal to MK (midpoint property)

Since \( M \) is the midpoint of \( \overline{JK} \), \( JM = MK \). So we set up the equation:
\( 48x + 25 = 43x + 35 \)

Step2: Solve for x

Subtract \( 43x \) from both sides:
\( 48x - 43x + 25 = 35 \)
\( 5x + 25 = 35 \)
Subtract 25 from both sides:
\( 5x = 35 - 25 \)
\( 5x = 10 \)
Divide both sides by 5:
\( x = \frac{10}{5} = 2 \)

Step3: Find MK by substituting x

Substitute \( x = 2 \) into the expression for \( MK \):
\( MK = 43x + 35 = 43(2) + 35 \)
\( MK = 86 + 35 = 121 \)

Answer:

\( 121 \)