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 \( \overline{IK} \), we have \( IJ + JK = IK \). Substituting the given expressions: \( 5x + 2x = x + 6 \).

Step2: Solve for \( x \)

Simplify left side: \( 7x = x + 6 \). Subtract \( x \) from both sides: \( 7x - x = 6 \) → \( 6x = 6 \). Divide by 6: \( x = 1 \).

Step3: Find length of \( \overline{JK} \)

Substitute \( x = 1 \) into \( JK = 2x \): \( JK = 2(1) = 2 \).

Answer:

2