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 m<span>easure 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
</span>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 = <span>9x-2
</span>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.
-----
Answer: HJ = 25, JK = 25, HK = 50
What is this asking I have no idea
