Question

k is the midpoint of $overline{jl}$.
$4z + 1$
$5z - 11$
j •
k
l
find jk, kl, and jl.
jk =
kl =

Explanation:

Step1: Use mid - point property

Since K is the mid - point of $\overline{JL}$, then $JK = KL$. So, $4z + 1=5z - 11$.

Step2: Solve for z

Subtract $4z$ from both sides: $1=5z - 4z-11$, which simplifies to $1 = z - 11$. Then add 11 to both sides, we get $z=12$.

Step3: Find JK

Substitute $z = 12$ into the expression for $JK$: $JK=4z + 1=4\times12 + 1=48 + 1=49$.

Step4: Find KL

Since $KL = JK$ (because K is the mid - point), $KL = 49$.

Step5: Find JL

$JL=JK + KL$, so $JL=49+49 = 98$.

Answer:

$JK = 49$
$KL = 49$
$JL = 98$