SOLUTION: The line joining the points (2,1) and (5,-8) is trisectedat the points P and Q. If the point P lies on the line 2x-y+k=0, find the value of k.

Question 1011414: The line joining the points (2,1) and (5,-8) is trisectedat the points P and Q. If the point P lies on the line 2x-y+k=0, find the value of k.
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Outline of the process:
(1) Distance between the two points
(2) Equation of the line with the points
(3) Equation for the description, one-third the distance from either point
(4) Solve the equation to find the unknown coordinate matching the description

One-third the distance from (2,1) to (5,8):

Their distance

, the general point (x, (7/3)x+1/3).

Point P is one-third distance from (2,1) to (5,8), here making (2,1) the choice for reference
to start from.

---some algebra steps---

--work through some more steps--

-
OR

y-coordinate which properly fits would be, if checking with a sketched graph, is based on .

Point P is the point and .

The question asked to find k, in the line containing P, being

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