SOLUTION: find the coordinates of the point P that lies along the directed line segment from A(3,4) TO B(6,10) and partitions the segment in the ratio 3 to 2

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Question 1009558: find the coordinates of the point P that lies along the directed line segment from A(3,4) TO B(6,10) and partitions the segment in the ratio 3 to 2
Answer by MathLover1(20849) About Me  (Show Source):
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find the coordinates of the point P that lies along the directed line segment from A(3,4) TO B(6,10) and partitions the segment in the ratio 3%3A+2
To find the point P that divides a segment AB into a particular ratio, determine the ratio k by writing the numerator over the sum of the numerator and the denominator of the given ratio. Next, find the rise and the run (slope) of the line. Finally, add k%2A+the_run to the x-coordinate of A and add k%2A+the+_rise to the y-coordinate of A. This process is summarized with the following formula.

(x,y)=(x%5B1%5D%2Bk%28x%5B2%5D-x%5B1%5D%29,y%5B1%5D%2Bk%28y%5B2%5D-y%5B1%5D%29)
so,
the ratio 3%3A+2=> partitions the segment into 5 congruent pieces
the slope of AB is run%2Frise=%2810-4%29%2F%286-3%29=6%2F3
find the coordinates of the point P ,
add 3%2F5 of the run to the x-coordinate of point A
and 3%2F5 of the rise to the y-coordinate of point A
run: %283%2F5%293=1.8
rise:%28+3%2F5%29+6=3.6
so, the coordinates of the point P are:

(3%2B1.8,4%2B3.6)
(4.8,7.6)
the ratio of AP%3APB is 3%3A2