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 the equation for \( x \)

Simplify the left - hand side of the equation: \( x+x + 6=18 \), which combines to \( 2x+6 = 18 \). Subtract 6 from both sides: \( 2x=18 - 6=12 \). Then divide both sides by 2: \( x=\frac{12}{2}=6 \).

Step3: Find the value of \( KL \)

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

Answer:

12