## 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

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

so thats your cordinates right?

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

(: