SOLUTION: What are the coordinates of the point that is 1/5 of the way from A(−7, −4) to B(3, 6)?

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Question 1023728: What are the coordinates of the point that is 1/5 of the way from A(−7, −4) to B(3, 6)?
Found 3 solutions by ikleyn, josgarithmetic, Alan3354:
Answer by ikleyn(52800) About Me  (Show Source):
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Some unknown point (x,y).

sqrt%28%28x%2B7%29%5E2%2B%28y%2B4%29%5E2%29=%281%2F5%29sqrt%28100%2B100%29
sqrt%28%28x%2B7%29%5E2%2B%28y%2B4%29%5E2%29=%281%2F5%29%2A10%2Asqrt%282%29
sqrt%28%28x%2B7%29%5E2%2B%28y%2B4%29%5E2%29=2%2Asqrt%282%29
%28x%2B7%29%5E2%2B%28y%2B4%29%5E2=8

Line AB is y-6=%28%286-%28-4%29%29%2F%283-%28-7%29%29%29%28x-3%29
y-6=1%2A%28x-3%29
y-6=x-3
y=x-3%2B6
y=x%2B3
Or some general point (x, x+3).

The previous, distance formula derived equation then becomes
%28x%2B7%29%5E2%2B%28x%2B3%2B4%29%5E2=8
%28x%2B7%29%5E2%2B%28x%2B7%29%5E2=8
2%28x%2B7%29%5E2=8
%28x%2B7%29%5E2=4
x%2B7=0%2B-+2
x=-7%2B-+2
EITHER x=-9 OR x=-5.


One of those will work and the other one will not work.
Take highlight%28x=-5%29. The corresponding y, being on line AB will be x%2B3=-5%2B3=-2; for the point (-5,-2).

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What are the coordinates of the point that is 1/5 of the way from A(-7,-4) to B(3,6)?
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Increase in x from -7 to 3 --> 10
Increase in y from -4 to 6 --> 10
1/5 of 10 = 2
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Add 2 to x & y of point A.
--> (-5,-2)