Question

point j is on line segment $overline{ik}$. given $ik = 5x$, $ij = 4$, and $jk = 4x$, determine the numerical length of $overline{ik}$.

Explanation:

Step1: Use segment - addition postulate

Since point J is on line segment $\overline{IK}$, then $IJ + JK=IK$. Substitute the given expressions: $4 + 4x=5x$.

Step2: Solve for x

Subtract $4x$ from both sides of the equation $4 + 4x=5x$. We get $4=5x - 4x$, so $x = 4$.

Step3: Find the length of $\overline{IK}$

Substitute $x = 4$ into the expression for $IK$. Since $IK = 5x$, then $IK=5\times4=20$.

Answer:

20