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davian
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
I think your description is incomplete, but I get the idea. Okay, let's look at it this way: |dw:1324417543699:dw|
J is supposed to be the midpoint of the line |LK|, and we know both its coordinates and the coordinates of point K.
oh sorry yea its suppose to be J is the midpoint of KL
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?
so i wud just use the points to find L?
That's right; given\[J:(-8,7),\]\[K:(3,4),\]can you find the equation of the line?
Remember the point-slope formula\[y=m(x-x_1)+y_1,\]where\[m=\frac{y_2-y_1}{x_2-x_1}.\]
you can yea, but im not sure what formula to use
First find m, and then find the equation. :) Tell me what you get.
That's correct;\[m=-\frac{3}{11}.\]
so thats your cordinates right?
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!
(We're almost done, too!)
i got -0.86 which i think is way off?..
For the equation of the line, I got\[y=-\frac{3}{11}x+\frac{53}{11}.\]Do you agree with this?
yea im sure you did it right im just not sure what u did?...(this is why geometry confuses me)
I only did one thing: I found the equation of the line formed by the points J and K.
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)
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! :)
o i got that equation but when i simplified it i got -0.86 for some reason
After distributing, you should get a term having an x in it:|dw:1324419228233:dw|
oh i changed -3/11 to a fraction thats why i got confused i think
i mean a decimal not a fraction
you simplify it more, and you get\[y=-\frac{3}{11}x+\frac{53}{11}\] :)
The final step is at hand! Are you ready for it?
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
If we go 11 units to the left of -8, what do we get?
Yes! Finally, plug -19 into the equation we obtained above, and you'll get the y-coordinate of point L! :)
y=m(x−x1)+y1, that formula?
This one\[y=-\frac{3}{11}x+\frac{53}{11}.\]:)
i got -4/11 ? is that right?
\[-\frac{3}{11}\cdot(-19)+\frac{53}{11}=\frac{57}{11}+\frac{53}{11}=\frac{110}{11}=10\]
Yeah, the signs can become a pain at times. ^^
haha yeah thank you for your help
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. :)
thank you soo much for walking through it and helping me i really appreciate it