Question

points j, k, and l are collinear. point k is between j and l, jl = 21z - 4, jk = 10z + 11, and kl = 4z + 6. find jk.

Explanation:

Step1: Use collinear - point property

Since $J$, $K$, and $L$ are collinear and $K$ is between $J$ and $L$, we have $JL=JK + KL$. So, $(21z - 4)=(10z + 11)+(4z + 6)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(10z + 11)+(4z + 6)=10z+4z + 11 + 6=14z + 17$. So the equation becomes $21z-4 = 14z + 17$.

Step3: Solve for $z$

Subtract $14z$ from both sides: $21z-14z-4=14z-14z + 17$, which simplifies to $7z-4 = 17$. Then add 4 to both sides: $7z-4 + 4=17 + 4$, so $7z=21$. Divide both sides by 7: $z=\frac{21}{7}=3$.

Step4: Find $JK$

Substitute $z = 3$ into the expression for $JK$. Since $JK = 10z+11$, then $JK=10\times3 + 11=30 + 11=41$.

Answer:

41