valiyuh Group Title m is the segment bisector of segment JK . JM= 1/8x , and JK= 3/4x-6 . How do i find MK? Help? one year ago one year ago

1. mathstudent55 Group Title

What does segment bisector mean?

2. valiyuh Group Title

its a line that divides a segment in half?

3. mathstudent55 Group Title

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

4. mathstudent55 Group Title

|dw:1377144056587:dw|

5. mathstudent55 Group Title

Ok?

6. mathstudent55 Group Title

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

7. valiyuh Group Title

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

8. mathstudent55 Group Title

Good. |dw:1377144680791:dw|

9. mathstudent55 Group Title

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

10. valiyuh Group Title

yes .

11. mathstudent55 Group Title

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

12. valiyuh Group Title

1/8x + 1/8x = 3/4x-6 like this?

13. mathstudent55 Group Title

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

14. mathstudent55 Group Title

$$\dfrac{1}{8}x + \dfrac{1}{8}x = \dfrac{3}{4}x - 6$$ Solve for x.

15. valiyuh Group Title

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

16. mathstudent55 Group Title

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

17. valiyuh Group Title

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

18. mathstudent55 Group Title

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

19. mathstudent55 Group Title

$$\dfrac{1}{4}x = \dfrac{3}{4}x - 6$$

20. mathstudent55 Group Title

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

21. valiyuh Group Title

it gave me -2x=-6?

22. mathstudent55 Group Title

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

23. mathstudent55 Group Title

$$\dfrac{1}{4}x - \dfrac{3}{4}x = - 6$$ $$-\dfrac{2}{4}x = - 6$$

24. valiyuh Group Title

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

25. mathstudent55 Group Title

Now you multiply both sides by -4/2.

26. mathstudent55 Group Title

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

27. mathstudent55 Group Title

Did you get an answer for x?

28. valiyuh Group Title

12?

29. mathstudent55 Group Title

Correct.

30. mathstudent55 Group Title

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.

31. valiyuh Group Title

yes thats correct.

32. mathstudent55 Group Title

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?

33. valiyuh Group Title

1.5?

34. mathstudent55 Group Title

Yes. MK = 12/8 = 1.5

35. mathstudent55 Group Title

You got it! Great job.

36. valiyuh Group Title

Thank you so much you really helped me !(:

37. mathstudent55 Group Title

You are very welcome.