Question

point j is on line segment (overline{ik}). given (jk = 2x), (ij = 5x), and (ik = x + 6), determine the numerical length of (overline{jk}).

Explanation:

Step1: Use segment addition postulate

Since \(J\) is on \(\overline{IK}\), then \(IJ + JK=IK\).
Substitute \(IJ = 5x\), \(JK = 2x\), and \(IK=x + 6\) into the equation: \(5x+2x=x + 6\).

Step2: Simplify the left - hand side

Combine like terms: \(7x=x + 6\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(7x-x=x + 6-x\), which gives \(6x=6\).
Divide both sides by \(6\): \(x=\frac{6}{6}=1\).

Step4: Find the length of \(JK\)

Substitute \(x = 1\) into \(JK = 2x\). So \(JK=2\times1 = 2\).

Answer:

\(2\)