anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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across
  • across
I think your description is incomplete, but I get the idea. Okay, let's look at it this way: |dw:1324417543699:dw|
across
  • across
J is supposed to be the midpoint of the line |LK|, and we know both its coordinates and the coordinates of point K.
anonymous
  • anonymous
oh sorry yea its suppose to be J is the midpoint of KL

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across
  • 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?
anonymous
  • anonymous
|dw:1324417943491:dw|
anonymous
  • anonymous
so i wud just use the points to find L?
across
  • across
That's right; given\[J:(-8,7),\]\[K:(3,4),\]can you find the equation of the line?
across
  • across
Remember the point-slope formula\[y=m(x-x_1)+y_1,\]where\[m=\frac{y_2-y_1}{x_2-x_1}.\]
anonymous
  • anonymous
you can yea, but im not sure what formula to use
anonymous
  • anonymous
ohh
across
  • across
First find m, and then find the equation. :) Tell me what you get.
anonymous
  • anonymous
i got -3/11 for M
across
  • across
That's correct;\[m=-\frac{3}{11}.\]
anonymous
  • anonymous
so thats your cordinates right?
across
  • 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!
across
  • across
(We're almost done, too!)
anonymous
  • anonymous
i got -0.86 which i think is way off?..
across
  • across
For the equation of the line, I got\[y=-\frac{3}{11}x+\frac{53}{11}.\]Do you agree with this?
anonymous
  • anonymous
yea im sure you did it right im just not sure what u did?...(this is why geometry confuses me)
across
  • across
I only did one thing: I found the equation of the line formed by the points J and K.
anonymous
  • anonymous
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)
across
  • 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! :)
anonymous
  • anonymous
o i got that equation but when i simplified it i got -0.86 for some reason
across
  • across
After distributing, you should get a term having an x in it:|dw:1324419228233:dw|
anonymous
  • anonymous
oh i changed -3/11 to a fraction thats why i got confused i think
anonymous
  • anonymous
i mean a decimal not a fraction
across
  • across
you simplify it more, and you get\[y=-\frac{3}{11}x+\frac{53}{11}\] :)
across
  • across
The final step is at hand! Are you ready for it?
anonymous
  • anonymous
Yes Ma'am
across
  • 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
across
  • across
If we go 11 units to the left of -8, what do we get?
anonymous
  • anonymous
-19?
across
  • across
Yes! Finally, plug -19 into the equation we obtained above, and you'll get the y-coordinate of point L! :)
anonymous
  • anonymous
y=m(x−x1)+y1, that formula?
across
  • across
This one\[y=-\frac{3}{11}x+\frac{53}{11}.\]:)
anonymous
  • anonymous
i got -4/11 ? is that right?
across
  • across
\[-\frac{3}{11}\cdot(-19)+\frac{53}{11}=\frac{57}{11}+\frac{53}{11}=\frac{110}{11}=10\]
anonymous
  • anonymous
ohh i added -57 to 53
across
  • across
Yeah, the signs can become a pain at times. ^^
anonymous
  • anonymous
haha yeah thank you for your help
across
  • 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. :)
anonymous
  • anonymous
thank you soo much for walking through it and helping me i really appreciate it
across
  • across
you're most welcome!
anonymous
  • anonymous
(:

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