Question

find the value of c and yz if y is between x and z.
xy = 11, yz = 4c, xz = 83

Explanation:

Step1: Use segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we know that \( XY + YZ = XZ \). Substituting the given values, we get \( 11 + 4c = 83 \).

Step2: Solve for \( c \)

Subtract 11 from both sides: \( 4c = 83 - 11 \). So \( 4c = 72 \). Then divide both sides by 4: \( c = \frac{72}{4} = 18 \).

Step3: Find \( YZ \)

We know \( YZ = 4c \), and we found \( c = 18 \), so substitute \( c \) into the equation: \( YZ = 4\times18 = 72 \).

Answer:

\( c = 18 \), \( YZ = 72 \)