To find JL when K is the midpoint of JL, set JK equal to KL, solve for x, then double the value of one segment since JK is equal to KL. The full length of JL is 78 units.
The question involves using the properties of line segments to find the length of the entire line segment JL when K is the midpoint. Since K is the midpoint of JL, JK is equal to KL. Given JK = 8x - 9 and KL = 2x + 27, we can set these two expressions equal to each other to find the value of x:
8x - 9 = 2x + 27.
Now, solving for x:
8x - 2x = 27 + 9
6x = 36
x = 6
Now that we have the value of x, we can substitute it back into either JK or KL to find the length of one segment:
JK = 8x - 9 = 8(6) - 9 = 48 - 9 = 39.
Since JK is equal to KL, JL, the full length of the segment, is 39 + 39, which is 78 units.
The complete question is- K is the midpoint of JL if: JK=8x-9 and KL=2x+27 find JL.