point j is on line segment $overline{ik}$. given $ik = 5x$, $ij = 4$, and $jk = 4x$, determine the numerical…
point j is on line segment $overline{ik}$. given $ik = 5x$, $ij = 4$, and $jk = 4x$, determine the numerical length of $overline{ik}$.
Answer
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:
$20$