K is the midpoint of JL JL=4x-2
and JK=7. find x, KL, and JL.
Very confused , can you please show steps to working out the problem
thank you so much steve
To find x, KL, and JL, we will use the properties of a midpoint.
1. Let's start by understanding the concept of a midpoint. A midpoint is a point on a line segment that divides the segment into two equal parts. In this case, K is the midpoint of JL, meaning that JK is equal to KL.
2. We are given that JK = 7, and we want to find x. We can set up an equation using the definition of a midpoint. Since JK = KL, we can write the equation: KL = 7.
3. Next, we are given that JL = 4x - 2. Since K is the midpoint of JL, we can use the midpoint formula, which states that the midpoint is the average of the two endpoints. So, we can set up the equation (JL/2) = KL.
4. Plugging in the values we know, we have: (4x - 2) / 2 = 7.
5. To solve for x, we can multiply both sides of the equation by 2 to get rid of the fraction: 4x - 2 = 7 * 2.
6. Simplifying further, we have: 4x - 2 = 14.
7. To isolate x, we can add 2 to both sides of the equation: 4x = 14 + 2.
8. Simplifying, we have: 4x = 16.
9. Finally, to solve for x, we divide both sides of the equation by 4: x = 16 / 4.
10. Solving further, x = 4.
So, the value of x is 4.
To find KL, substitute the value of x into KL = 7: KL = 7.
Therefore, KL = 7.
To find JL, substitute the value of x into JL = 4x - 2: JL = 4(4) - 2.
Simplifying further, JL = 16 - 2.
Therefore, JL = 14.
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if K is the midpoint of JL, JK=8x+11 and KL=14x-1 find JL
JL is the whole length, so JK is half the length. So,
7+7 = 4x-2
4x = 16
x = 4
So, JL = 4*4-2 = 14
JK = KL = 7
Actually, since they told us that JK=7, we knew right away that JL was 14, since JK was half of JL. All that nonsense about x and stuff was superfluous.