SOLUTION: Point J is located at (2,5) and point K is located at (4,19). What are the coordinates of the point that partitions the directed line segment JK in a 3:2 ratio?

Question 1064977: Point J is located at (2,5) and point K is located at (4,19).
What are the coordinates of the point that partitions the directed line segment JK in a 3:2 ratio?
Found 4 solutions by Fombitz, josgarithmetic, ikleyn, MathTherapy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
So the point P is 3/5 of the distance from J to K (starting at J).
Find the x distance,

Divide by 5,

Now move 3 x divisions from J,

Similarly for y,

So the point P is
(,)

Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
Line JK is

Using Distance Formula for "the point that partitions the directed line segment JK in a 3:2 ratio",

Substitute, simplify, and solve first for x. Choose the solution which would be between J and K, and then evaluate y.

.

.

(Discriminant, )

Finding y:

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Ignore the solution by "josgarithmetic".

His approach will lead you to "nowhere".

        "JOSGARITHMETIC" !!     STOP WRITING NONSENSE !!!

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Point J is located at (2,5) and point K is located at (4,19).
What are the coordinates of the point that partitions the directed line segment JK in a 3:2 ratio?

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