3. If K is the midpoint of HJ, HK = x + 6, and HJ = 4x − 6, then KJ = ? (4 pts)
To find KJ, we can use the fact that K is the midpoint of HJ. This means that the length of HK is equal to the length of KJ.
Given that HK = x + 6, we can set it equal to KJ: x + 6 = KJ
Now, we are also given that HJ = 4x - 6. Since K is the midpoint, we can set up an equation that represents the relationship between HJ, HK, and KJ:
HJ = HK + KJ
Substituting the given values, we have:
4x - 6 = (x + 6) + KJ
Simplifying the equation:
4x - 6 = x + 6 + KJ
4x - 6 - x - 6 = x + 6 + KJ - x - 6
3x - 12 = KJ
Now, we can substitute the value of HK into this equation to find KJ:
3x - 12 = x + 6
3x - x = 6 + 12
2x = 18
x = 9
Now, we can substitute the value of x back into the equation for KJ:
KJ = 3x - 12
KJ = 3(9) - 12
KJ = 27 - 12
KJ = 15
Therefore, KJ is equal to 15.