Question

find the value of a and yz if y is between x and z. xy = 3a - 4, yz = 6a + 2, xz = 5a + 22

Explanation:

Step1: Use segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substitute the given expressions:
\( (3a - 4) + (6a + 2) = 5a + 22 \)

Step2: Simplify left side

Combine like terms: \( 3a + 6a - 4 + 2 = 9a - 2 \). So the equation becomes:
\( 9a - 2 = 5a + 22 \)

Step3: Solve for \( a \)

Subtract \( 5a \) from both sides: \( 9a - 5a - 2 = 22 \) → \( 4a - 2 = 22 \). Add 2 to both sides: \( 4a = 24 \). Divide by 4: \( a = 6 \)

Step4: Find \( YZ \)

Substitute \( a = 6 \) into \( YZ = 6a + 2 \):
\( YZ = 6(6) + 2 = 36 + 2 = 38 \)

Answer:

\( a = 6 \), \( YZ = 38 \)