Question

7 use the diagram to answer the question below.
xm = 10x + 6 and my = 6x + 22
if m is the midpoint of segment \\(\overline{xy}\\), solve for \\(\overline{xy}\\).
xy = \\(square\\)

Explanation:

Step1: Set \( XM = MY \) (midpoint property)

Since \( M \) is the midpoint of \( \overline{XY} \), \( XM = MY \). So we set up the equation:
\( 10x + 6 = 6x + 22 \)

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides:
\( 10x - 6x + 6 = 22 \)
\( 4x + 6 = 22 \)

Subtract 6 from both sides:
\( 4x = 22 - 6 \)
\( 4x = 16 \)

Divide both sides by 4:
\( x = \frac{16}{4} = 4 \)

Step3: Find \( XM \) and \( MY \)

Substitute \( x = 4 \) into \( XM = 10x + 6 \):
\( XM = 10(4) + 6 = 40 + 6 = 46 \)

Since \( XM = MY \), \( MY = 46 \)

Step4: Calculate \( XY \)

\( XY = XM + MY \) (segment addition postulate). Since \( XM = MY = 46 \):
\( XY = 46 + 46 = 92 \)

Answer:

\( 92 \)