Point i is on line segment hj. given h i = x, h j = 3x – 9, and
ij = x + 5, determine the numerical length of hj.

The numerical length of HJ is 33

The given parameters;

distance of HI = x

distance of HJ = 3x - 9

distance of IJ = x + 5

To find:

A sketch of the positions of the line segments is shown below;

|<x>|<x+5>|

HIJ

The value of x will be calculated by setting up the following equation;

HI + IJ = HJ

x + x + 5 = 3x - 9

2x + 5 = 3x - 9

collect similar terms together;

2x - 3x = -9-5

-x = -14

x = 14

The numerical length of HJ is calculated as;

HJ  = 3(14) - 9

HJ = 42 - 9

HJ = 33

Thus, the numerical length of HJ is 33

Learn more here: link

HJ = 33

Step-by-step explanation:

Given that point I is on segment HJ, then

HJ = HI + IJ ← substitute values

3x - 9 = x + x + 5, that is

3x - 9 = 2x + 5 ( subtract 2x from both sides )

x - 9 = 5 ( add 9 to both sides )

x = 14

Hence

HJ = 3x - 9 = (3 × 14) - 9 = 42 - 9 = 33

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction