## davian Group Title J is the midpoint of The coordinates of J are (-8,7) and the coordinates of K are (3,4) find the coordinates of L. can someone help me? i get really confused with geometry and im trying to finish this final and im not sure how to solve this problem 2 years ago 2 years ago

1. across Group Title

I think your description is incomplete, but I get the idea. Okay, let's look at it this way: |dw:1324417543699:dw|

2. across Group Title

J is supposed to be the midpoint of the line |LK|, and we know both its coordinates and the coordinates of point K.

3. davian Group Title

oh sorry yea its suppose to be J is the midpoint of KL

4. across Group Title

A good way to tackle this would be to find the equation of the line formed by the points J and K, that is, find the equation of the line |JK|. Do you know how to do that?

5. davian Group Title

|dw:1324417943491:dw|

6. davian Group Title

so i wud just use the points to find L?

7. across Group Title

That's right; given$J:(-8,7),$$K:(3,4),$can you find the equation of the line?

8. across Group Title

Remember the point-slope formula$y=m(x-x_1)+y_1,$where$m=\frac{y_2-y_1}{x_2-x_1}.$

9. davian Group Title

you can yea, but im not sure what formula to use

10. davian Group Title

ohh

11. across Group Title

First find m, and then find the equation. :) Tell me what you get.

12. davian Group Title

i got -3/11 for M

13. across Group Title

That's correct;$m=-\frac{3}{11}.$

14. davian Group Title

15. across Group Title

That's the slope of the line we're trying to find. To find the equation of the line, we substitute these values into the point-slope equation:$y=-\frac{3}{11}(x-3)+4.$Let's simplify!

16. across Group Title

(We're almost done, too!)

17. davian Group Title

i got -0.86 which i think is way off?..

18. across Group Title

For the equation of the line, I got$y=-\frac{3}{11}x+\frac{53}{11}.$Do you agree with this?

19. davian Group Title

yea im sure you did it right im just not sure what u did?...(this is why geometry confuses me)

20. across Group Title

I only did one thing: I found the equation of the line formed by the points J and K.

21. davian Group Title

i understand that, im just not sure what steps u used, after we got -3/11 i got lost after that (sorry i dont mean to make things difficult)

22. across Group Title

hey, no probs :) right after we found m=-3/11, i plugged all the values we know into the point-slope equation$y=m(x-x_1)+y_1.$we know that $$m=-3/11$$, $$x_1=3$$ and $$y_1=4$$. After plugging those values into the equation, we get$y=-\frac{3}{11}(x-3)+4.$Then I simplified that! :)

23. davian Group Title

o i got that equation but when i simplified it i got -0.86 for some reason

24. across Group Title

After distributing, you should get a term having an x in it:|dw:1324419228233:dw|

25. davian Group Title

oh i changed -3/11 to a fraction thats why i got confused i think

26. davian Group Title

i mean a decimal not a fraction

27. across Group Title

you simplify it more, and you get$y=-\frac{3}{11}x+\frac{53}{11}$ :)

28. across Group Title

The final step is at hand! Are you ready for it?

29. davian Group Title

Yes Ma'am

30. across Group Title

Now, we know that the x-distance from point J to point K is 11, right? J:(-8*,7) K:(3*,4) 8+3=11

31. across Group Title

If we go 11 units to the left of -8, what do we get?

32. davian Group Title

-19?

33. across Group Title

Yes! Finally, plug -19 into the equation we obtained above, and you'll get the y-coordinate of point L! :)

34. davian Group Title

y=m(x−x1)+y1, that formula?

35. across Group Title

This one$y=-\frac{3}{11}x+\frac{53}{11}.$:)

36. davian Group Title

i got -4/11 ? is that right?

37. across Group Title

$-\frac{3}{11}\cdot(-19)+\frac{53}{11}=\frac{57}{11}+\frac{53}{11}=\frac{110}{11}=10$

38. davian Group Title

ohh i added -57 to 53

39. across Group Title

Yeah, the signs can become a pain at times. ^^

40. davian Group Title

haha yeah thank you for your help

41. across Group Title

Anyway, there's your answer! The coordinates of point L are (-19,10). I know the process may feel a bit lengthy *looks up*, but it's really not when you give it a second look. :)

42. davian Group Title

thank you soo much for walking through it and helping me i really appreciate it

43. across Group Title

you're most welcome!

44. davian Group Title

(: