Question

persevere point k is between points j and l. if jk = x² - 4x, kl = 3x - 2, and jl = 28, find jk and kl

Explanation:

Step1: Use segment addition postulate

Since \( K \) is between \( J \) and \( L \), we have \( JK + KL = JL \). Substitute the given expressions: \( x^2 - 4x + 3x - 2 = 28 \). Simplify to get \( x^2 - x - 30 = 0 \).

Step2: Solve the quadratic equation

Factor \( x^2 - x - 30 = 0 \) as \( (x - 6)(x + 5) = 0 \). So \( x = 6 \) or \( x = -5 \).

Step3: Check valid \( x \)

For \( x = -5 \), \( KL = 3(-5) - 2 = -17 \) (length can't be negative). For \( x = 6 \), \( JK = 6^2 - 4(6) = 12 \), \( KL = 3(6) - 2 = 16 \). Check \( 12 + 16 = 28 \), which matches \( JL \).

Answer:

\( JK = 12 \), \( KL = 16 \)