m is the midpoint of segment jk. jm=x/8 and jk=3x/4 subtracted by 6. find mk
JM=MK=JK/2
x/8 = (3x/4-6)/2
x/8 = (3X/4-24/4)/2
x/8 = 3x/8 - 24/8
x = 3x - 24
x-3x = -24
-2x = -24
x = 12
12/8 = 1.5 = JM = MK
To find the length of MK, we can use the midpoint formula:
Midpoint formula: M = (x1 + x2)/2, (y1 + y2)/2
Given that point M is the midpoint of segment JK, let's assign coordinates to point J and point K:
Let J = (x1, y1) and K = (x2, y2)
Since we're only interested in the length of MK, we don't need the y-coordinates.
From the given information, we know that JM = x/8, and JK = (3x/4) - 6.
Now, let's find the x-coordinates of points J and K:
JM = JK
x/8 = (3x/4) - 6
To solve for x, let's first eliminate the denominators by multiplying both sides of the equation by 8:
8 * (x/8) = 8 * ((3x/4) - 6)
x = 6x - 48
Now, let's bring all the x terms to one side of the equation:
x - 6x = -48
-5x = -48
To isolate x, we need to divide both sides of the equation by -5:
x = -48 / -5
x = 9.6
Now that we have the value of x, we can find the length of MK by substituting it back into the equation for JK:
JK = (3x/4) - 6
JK = (3 * 9.6 / 4) - 6
JK = (28.8 / 4) - 6
JK = 7.2 - 6
JK = 1.2
Since MK is the other half of JK (since M is the midpoint), MK will be equal to JK:
MK = JK = 1.2
Therefore, the length of MK is 1.2.
To find MK, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (m) between two points (J and K) can be found by taking the average of their respective x-coordinates and the average of their respective y-coordinates.
Here, we are given the lengths JM and JK in terms of x. To find MK, we need to determine the length of MK using the given information.
Let's start by setting up an equation based on the midpoint formula:
MK = 2 * JM
Since JM is given as x/8,
MK = 2 * (x/8)
Simplifying further,
MK = x/4
Therefore, the length of MK is given by x/4.
if m is the midpoint, jm = mk, so
x/8 = 3x/4 - 6
x = 48/5
jm = mk = 6/5