valiyuh
m is the segment bisector of segment JK . JM= 1/8x , and JK= 3/4x6 . How do i find MK? Help?



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mathstudent55
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What does segment bisector mean?

valiyuh
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its a line that divides a segment in half?

mathstudent55
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Right. In this case, I think M is simply a point, but it still cuts the segment JK into two congruent segments.

mathstudent55
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dw:1377144056587:dw

mathstudent55
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Ok?

mathstudent55
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Since M is a bisector, what do you know about the length of JM and the length of KM?

valiyuh
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Well i know that since m is the bisector both sides are equal which mean that since JM is 1/8x MK is also 1/8x

mathstudent55
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Good.
dw:1377144680791:dw

mathstudent55
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Form the figure you see that JM + MK = JK, right?

valiyuh
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yes .

mathstudent55
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Great.
Below JM, MK, and JK, can you write what each one is equal to?
Copy my line below and write it below that line.
JM + MK = JK

valiyuh
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1/8x + 1/8x = 3/4x6 like this?

mathstudent55
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Exactly. That is the equation you must solve now to find x.

mathstudent55
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\( \dfrac{1}{8}x + \dfrac{1}{8}x = \dfrac{3}{4}x  6\)
Solve for x.

valiyuh
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This is the part were im getting confused? Do i add both 1/8x to get 2/8x? or am i wrong?

mathstudent55
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Yes, you are correct.
\(\dfrac{2}{8}x = \dfrac{3}{4}x  6 \)
The fraction on the left can be reduced.

valiyuh
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alright so now i subtract the 3/4 to the other side so now its 2/8  3/4?

mathstudent55
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Why don't you reduce the 2/8 fraction first?

mathstudent55
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\(\dfrac{1}{4}x = \dfrac{3}{4}x  6 \)

mathstudent55
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Now the fractions have a common denominator.
Now you can subtract (3/4)x over to the left side.

valiyuh
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it gave me 2x=6?

mathstudent55
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What happened to the denominator of 4?
You subtracted 1/4  3/4, not 1  3.

mathstudent55
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\(\dfrac{1}{4}x  \dfrac{3}{4}x =  6 \)
\(\dfrac{2}{4}x =  6 \)

valiyuh
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oh okay i see and from there i cancel the 2/4x and take it to the other side having 6/2/4 right?

mathstudent55
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Now you multiply both sides by 4/2.

mathstudent55
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\( \dfrac{4}{2}\left( \dfrac{2}{4}x \right) = \dfrac{4}{2}( 6) \)

mathstudent55
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Did you get an answer for x?

valiyuh
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12?

mathstudent55
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Correct.

mathstudent55
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After you multiply out the right side, you get x = 12.
That's not the final answer of the problem, because the problem asks what is MK.

valiyuh
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yes thats correct.

mathstudent55
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Above, you had written an expression for MK in terms of x. Now you know x, so you can find MK.
MK = (1/8)x, and x = 12, so what is MK?

valiyuh
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1.5?

mathstudent55
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Yes.
MK = 12/8 = 1.5

mathstudent55
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You got it! Great job.

valiyuh
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Thank you so much you really helped me !(:

mathstudent55
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You are very welcome.