Point K is on line segment ‾JL. Given JK = 2x - 2, KL = x - 9, and JL = 2x + 8, determine the numerical length of ‾KL.

Point K is on line segment ‾JL. Given JK = 2x - 2, KL = x - 9, and JL = 2x + 8, determine the numerical length of ‾KL.

Question
Analytic geometry
asked 2021-02-01

Point K is on line segment \(\overline{JL}\). Given \(JK = 2x - 2, KL = x - 9,\ and\ JL = 2x + 8,\) determine the numerical length of \(\overline{KL}\).

Answers (1)

2021-02-02

By Angle Addition Postulate,
\(JL=JK+KL\)
Substitute given expressions:
\(2x+8=(2x−2)+(x−9)\)
Solve for x:
\(2x+8=3x−11\)
\(−x+8=−11\)
\(−x=−19\)
\(x=19\)
Hence,
\(KL=19−9\)
\(KL=10\)

0

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