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 $\overline{IK}$, we know that $IJ + JK=IK$.
Substitute the given expressions: $4 + 4x=5x$.

Step2: Solve for $x$

Subtract $4x$ from both sides of the equation $4 + 4x=5x$.
$4+4x - 4x=5x - 4x$, which gives $x = 4$.

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

We know that $IK = 5x$. Substitute $x = 4$ into the expression for $IK$.
$IK=5\times4$.

Answer:

$20$