Question

points j, k, and l are collinear. point k is between j and l, jk = 10z + 8, jl = 21z − 3, and kl = z + 9. find jk, kl, and jl.

Explanation:

Step1: Use segment addition postulate

Since K is between J and L, \( JL = JK + KL \). Substitute the given expressions: \( 21z - 3=(10z + 8)+(z + 9) \)

Step2: Simplify and solve for z

Simplify the right - hand side: \( 21z-3 = 11z + 17 \). Subtract \( 11z \) from both sides: \( 21z-11z-3=11z - 11z+17 \), which gives \( 10z-3 = 17 \). Add 3 to both sides: \( 10z-3 + 3=17 + 3 \), so \( 10z=20 \). Divide both sides by 10: \( z = 2 \)

Step3: Find JK

Substitute \( z = 2 \) into \( JK = 10z+8 \): \( JK=10\times2 + 8=20 + 8 = 28 \)

Step4: Find KL

Substitute \( z = 2 \) into \( KL=z + 9 \): \( KL=2 + 9=11 \)

Step5: Find JL

Substitute \( z = 2 \) into \( JL = 21z-3 \): \( JL=21\times2-3=42 - 3 = 39 \) (We can also verify using \( JL=JK + KL=28 + 11 = 39 \))

Answer:

\( JK = 28 \), \( KL = 11 \), \( JL = 39 \)