Question

1. given a is between y and z and ya = 5.5, az = 2x, and yz = 41.5, find az

a 9
b 18
c 36
d 72

Explanation:

Step1: Use the segment - addition postulate

Since \(A\) is between \(Y\) and \(Z\), by the segment - addition postulate \(YA + AZ=YZ\).
Substitute \(YA = 5.5\), \(AZ = 2x\), and \(YZ = 41.5\) into the equation: \(5.5+2x = 41.5\).

Step2: Solve the equation for \(x\)

Subtract \(5.5\) from both sides of the equation:
\(2x=41.5 - 5.5\).
\(2x=36\).
Divide both sides by \(2\): \(x = 18\).

Step3: Find the length of \(AZ\)

Since \(AZ = 2x\) and \(x = 18\), then \(AZ=2\times18\).

Answer:

\(36\), so the answer is C.