Question

question point i is on line segment hj. given hi = x, ij = 2x + 9, and hj = 4x, determine the numerical length of ij. answer attempt 1 out of 2 ij = submit answer watch video show examples

Explanation:

Step1: Use segment - addition postulate

Since $HJ=HI + IJ$, we substitute the given expressions: $4x=x+(2x + 9)$.

Step2: Solve the equation for x

First, simplify the right - hand side: $4x=x + 2x+9$, which gives $4x=3x + 9$. Then subtract $3x$ from both sides: $4x-3x=3x + 9-3x$, so $x = 9$.

Step3: Find the length of 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