Suppose J is between H and K. Use the Segment Addition Postulate to solve or x. Then find the length of each segment.
HJ= 2x+1/3
JK= 5x+2/3
KH= 12x-4
kH=JK+HJ
12x-4=5x+2/3 +2x+1/3
12x-4=7x+1
solve for x. Then, go back and substitute this in the original expressions to find HJ,JK,KH
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To solve for x using the Segment Addition Postulate, we start by noting that J is between H and K. According to the postulate, the sum of the lengths of segment HJ and segment JK is equal to the length of segment HK.
Therefore, we can write the equation as follows:
HJ + JK = HK
Substituting the given lengths, we have:
(2x + 1/3) + (5x + 2/3) = 12x - 4
Now we can solve for x:
2x + 1/3 + 5x + 2/3 = 12x - 4
Combining like terms, we get:
7x + 1 = 12x - 4
Moving the variables to one side and the constants to the other side:
7x - 12x = -4 - 1
Simplifying:
-5x = -5
Dividing both sides by -5:
x = 1
Now that we have found the value of x, we can substitute it back into the original expressions to find the lengths of the segments.
HJ = 2x + 1/3
HJ = 2(1) + 1/3
HJ = 2 + 1/3
HJ = 7/3
JK = 5x + 2/3
JK = 5(1) + 2/3
JK = 5 + 2/3
JK = 17/3
KH = 12x - 4
KH = 12(1) - 4
KH = 12 - 4
KH = 8
Therefore, the lengths of the segments are:
HJ = 7/3
JK = 17/3
KH = 8