Question

1. points j, k, and l are collinear. point k lies between j and l. find kl if jk = x, kl = x - 6, jl = 18

Explanation:

Step1: Use segment addition postulate

Since \( J \), \( K \), \( L \) are collinear and \( K \) is between \( J \) and \( L \), we have \( JK + KL = JL \). Substituting the given values \( JK = x \), \( KL = x - 6 \), and \( JL = 18 \), we get the equation \( x+(x - 6)=18 \).

Step2: Solve for \( x \)

Simplify the left - hand side of the equation: \( x+x - 6=18 \), which combines to \( 2x-6 = 18 \). Add 6 to both sides: \( 2x-6 + 6=18 + 6 \), so \( 2x=24 \). Divide both sides by 2: \( \frac{2x}{2}=\frac{24}{2} \), which gives \( x = 12 \).

Step3: Find \( KL \)

We know that \( KL=x - 6 \), and we found that \( x = 12 \). Substitute \( x = 12 \) into the expression for \( KL \): \( KL=12-6=6 \).

Answer:

\( 6 \)