Respuesta :
The length of the line segment is 33 units.
A line segment is defined as a part of a straight line which is bounded by two distinct points.
In cartesian plane the distance between two points on a line is calculated by the distance formula.
Given that point I lies on the line-segment HJ.
Length of HI is x , length of HJ is 3x-9 and length of IJ is x+5 .
Now we know that if I is at any point on the straight line HJ then
HI + IJ = HJ
Now we can substitute the values to get a linear equation in x:
∴x + (x+5) = 3x - 9
or, 2x + 5 = 3x - 9
or, 2x - 3x = - 9 - 5
or, - x = - 14
or, x = 14
Therefore length of HJ = 3x - 9 = (3×14) - 9 = 33.
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