SOLUTION: Find the equation that is satisfied by the coordinates of each point. A rod PQ of the length 12 moves so that P is always on the Y-axis and Q always on the X-axis. A point M on PQ

Question 1131594: Find the equation that is satisfied by the coordinates of each point. A rod PQ of the length 12 moves so that P is always on the Y-axis and Q always on the X-axis. A point M on PQ is 2/3 of the way from P to Q. What equation is satisfied by the coordinates of M?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
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From the length of the rod, you know,

and then you know that for the x coordinate,

and for the y coordinate,

So plugging back into the length equation,

Just to verify,
when ,, the point Q is at the origin, PQ lies entirely on the y axis,

Two solutions : ,
Two thirds from P to Q would be since P is at (0,12) then M should be at (0,12-8)=(0,4), which is consistent to the answer from the equation. P could also be at (0,-12). Similary 2/3 from P to Q would be (0,-12+8)=(0,-4).
You can do the same check when PQ is entirely on the x-axis just to verify ()

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