Question

k is the midpoint of $overline{jl}$. if $jk = x + 2$ and $kl = 2x - 4$, what is $kl?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(K\) is the mid - point of \(\overline{JL}\), then \(JK = KL\). So we set up the equation \(x + 2=2x - 4\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(x+2 - x=2x - 4 - x\), which simplifies to \(2=x - 4\). Then add 4 to both sides: \(2 + 4=x-4 + 4\), so \(x = 6\).

Step3: Find the value of \(KL\)

Substitute \(x = 6\) into the expression for \(KL\). Since \(KL=2x - 4\), then \(KL=2\times6 - 4\).
Calculate \(2\times6 - 4=12 - 4=8\).

Answer:

8