Question

point I is on line segment HJ. GIVEN IJ = 3× + 3, HI = 3× - 1, and HJ = 3× + 8, determine the numerical length of HJ.

Answer 1

Given, IJ = 3x + 3, HI = 3x - 1, and HJ = 3x + 8.

Since I is a point on line segment HJ, we can write

$HJ=HI+IJ$$\begin{gathered} 3x+8=(3x-1)+(3x+3) \\ 3x+8=6x+2 \\ 8-2=6x-3x \\ 6=3x \\ 2=x \end{gathered}$

Put x=2 in HJ=3x+8.

$\begin{gathered} HJ=3\times2+8 \\ HJ=6+8 \\ =14 \end{gathered}$

Therefore, the numerical length of HJ is 14.