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J is the midpoint of HK¯¯¯¯¯¯¯ . What are HJ, JK, and HK?
The image consists of a segment HK and point J is between points H and K. Measure of segment HJ is 9x-2 and that of segment JK is 4x+13.

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ali015
Since J is the midpoint of HK, that means HK is split into two sections HJ and JK that are the same length.

1) You are told that the measure of segment HJ = 9x-2 and that of segment JK = 4x+13. Since you also know they are equal lengths, you can set these equations equal to each other to find the value of x!
HJ = JK
9x-2 = 4x+13
5x = 15
x = 3

2) Now you know x = 3. Plug that into your given equations for HJ and JK to find the length of each segment (or a shortcut would be to find one of them, and then you also know the other is the same length. I'm doing both, just to make sure I don't make a silly mistake!):
HJ = 9x-2 
HJ = 9(3) - 2
HJ = 27 - 2
HJ = 25

JK = 4x + 13
JK = 4(3) + 13
JK = 12 + 13
JK = 25

3) Finally, the length of HK is just the length of HJ + JK, or HK = 25 + 25 = 50.

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Answer: HJ = 25, JK = 25, HK = 50
  • Step 1: We solve for x

According to the midpoint rule,

HJ = JK

HJ = 9x - 2

JK = 4x + 13

Hence,

HJ = JK

9x - 2 = 4x + 13

Collect like terms

9x - 4x = 13 + 2

5x = 15

Divide both sides by 5

5x/5 = 15/5

x = 3

  • Step 2: We solve for HJ

HJ = 9x - 2

x = 3

HJ = (9 x 3) - 2

HJ = 27 - 2

HJ = 25

  • Step 3: We solve for JK

JK = 4x + 13

x = 3

JK = (4 x 3) + 13

JK = 12 + 13

JK = 25

  • Step 4: We solve for HK

HK = HJ + JK

HK = 25 + 25

HK = 50

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https://brainly.com/question/23214457

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