## davian 3 years ago 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

1. across

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

2. across

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

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

4. across

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

|dw:1324417943491:dw|

6. davian

so i wud just use the points to find L?

7. across

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

8. across

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

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

10. davian

ohh

11. across

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

12. davian

i got -3/11 for M

13. across

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

14. davian

15. across

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

(We're almost done, too!)

17. davian

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

18. across

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

19. davian

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

20. across

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

21. davian

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

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

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

24. across

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

25. davian

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

26. davian

i mean a decimal not a fraction

27. across

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

28. across

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

29. davian

Yes Ma'am

30. across

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

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

32. davian

-19?

33. across

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

34. davian

y=m(x−x1)+y1, that formula?

35. across

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

36. davian

i got -4/11 ? is that right?

37. across

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

38. davian

ohh i added -57 to 53

39. across

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

40. davian

haha yeah thank you for your help

41. across

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

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

43. across

you're most welcome!

44. davian

(: