Question

point i is on line segment $overline{hj}$. given $hi = x, ij = 2x + 9$, and $hj = 4x$, determine the numerical length of $overline{ij}$.

Explanation:

Step1: Use segment - addition postulate

Since point I is on line segment $\overline{HJ}$, we have $HI + IJ=HJ$. Substitute the given expressions: $x+(2x + 9)=4x$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+2x + 9=3x + 9$. So, $3x + 9=4x$.

Step3: Solve for x

Subtract $3x$ from both sides of the equation: $3x+9-3x=4x - 3x$. We get $x = 9$.

Step4: Find the length of $\overline{IJ}$

Substitute $x = 9$ into the expression for $IJ$. Since $IJ=2x + 9$, then $IJ=2\times9+9$.
Calculate $2\times9+9=18 + 9=27$.

Answer:

27