Question

If K is the midpoint of JL, JK = 8x + 11 and KL = 14x – 1, find JL.​

Answer 1

Answer:

$JL=54$

Step-by-step explanation:

We are given that K is the midpoint of JL. Using this information, we want to find JL.

By the definition of midpoint, this means that:

$JK=KL$

Substitute them for their equations:

$8x+11=14x-1$

Solve for x. Subtract 8x from both sides:

$11=6x-1$

Add 1 to both sides:

$6x=12$

And divide both sides by 6. Hence:

$x=2$

JL is the sum of JK and KL. Hence:

$JK+KL=JL$

Since JK = KL, substitute either one for the other:

$JK+(JK)=2JK=JL$

Substitute JK for its equation:

$2(8x+11)=JL$

Since we know that x = 2:

$2(8(2)+11)=2(16+11)=2(27)=54=JL$

Thus:

$JL=54$