SOLUTION: If M (3,6) and N (9,0) what are the coordinates of the point L if it lies 2/3 of the way from M to N

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Question 830754: If M (3,6) and N (9,0) what are the coordinates of the point L if it lies 2/3 of the way from M to N
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Part-way through the solution,

The line MN :
m=(6-0)/(3-9)=-1.
if y=mx+b,then b=y-mx.
pick either point to get b.
b=0-(-1)9
b=9.
The line MN is y=-x%2B9.

Now, you want some point ON THE LINE MN, y=-x+9, which is 2/3 of the length distance from M(3,6). Use the distance formula, to first find the distance MN.

MN+=+sqrt%28%280-6%29%5E2%2B%289-3%29%5E2%29
sqrt%2836%2B36%29
sqrt%2872%29
sqrt%282%2A36%29
MN=highlight_green%286%2Asqrt%282%29%29
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%282%2F3%29%2A%28MN%29=2%2Asqrt%282%29-------Use this as a target value, and use distance formula again; but now, you have some unknown point, (x,-x+9) and the known point, (3,6), and you want the distance between them to be 2%2Asqrt%282%29.

If you understand all of that clearly, then you know what to do. Note, the variable point to be found, involves the line MN; the x coordinate as unknown, and the resulting y coordinate as -x+9.
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You will get two solutions for x and one of them will be what you want but the other will not be.