Question

drawing is not to scale.
if a,b,c are collinear, ac = 5z + 2, bc = 3z + 3 and ab = 53
find z and ac
z=
ac=

Explanation:

Step1: Use segment addition postulate

Since \(A\), \(B\), \(C\) are collinear, \(AB = AC+BC\). Substitute \(AC = 5z + 2\), \(BC=3z + 3\), and \(AB = 53\) into the equation:
\(53=(5z + 2)+(3z + 3)\)

Step2: Simplify the equation

Combine like - terms: \(53=5z+3z + 2 + 3\), so \(53 = 8z+5\)
Subtract \(5\) from both sides: \(53−5=8z\), \(48 = 8z\)

Step3: Solve for \(z\)

Divide both sides by \(8\): \(z=\frac{48}{8}=6\)

Step4: Find \(AC\)

Substitute \(z = 6\) into the formula for \(AC\): \(AC=5z + 2\)
\(AC=5\times6+2=30 + 2=32\)

Answer:

\(z = 6\)
\(AC = 32\)