If K is the midpoint of JL, JK= 8x + 11 and KL = 14x-1, find JL
The Correct Answer and Explanation is:
To find the length of JLJLJL, we need to use the information that KKK is the midpoint of JLJLJL. When KKK is the midpoint, it divides the segment JLJLJL into two equal parts. So, we can set the lengths JKJKJK and KLKLKL equal to each other:JK=KLJK = KLJK=KL
Now, we are given the expressions for JKJKJK and KLKLKL:JK=8x+11JK = 8x + 11JK=8x+11KL=14x−1KL = 14x – 1KL=14x−1
We can set these two equal to each other:8x+11=14x−18x + 11 = 14x – 18x+11=14x−1
Step 1: Solve for xxx
To solve for xxx, we first isolate xxx on one side. Subtract 8x8x8x from both sides:11=6x−111 = 6x – 111=6x−1
Next, add 1 to both sides:12=6×12 = 6×12=6x
Now, divide both sides by 6:x=2x = 2x=2
Step 2: Find the Length of JLJLJL
Now that we know x=2x = 2x=2, we can substitute it back into either the expression for JKJKJK or KLKLKL to find the length of one part of the segment. Let’s substitute into JKJKJK:JK=8x+11=8(2)+11=16+11=27JK = 8x + 11 = 8(2) + 11 = 16 + 11 = 27JK=8x+11=8(2)+11=16+11=27
Since KKK is the midpoint, the total length of JLJLJL is twice the length of JKJKJK (or KLKLKL):JL=2×JK=2×27=54JL = 2 \times JK = 2 \times 27 = 54JL=2×JK=2×27=54
Final Answer:
The length of JLJLJL is 54 units.
