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Point P is located at (2, 2) and point T is located at (7, 17).  What are the coordinates of the point that partitions the directed line segment PT in a 3:2 ratio?

 Feb 18, 2020
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If we have a 3:2  ratio....then  PT  can be divided into 5 equal parts.....

 

And the distance from P to the partition point  must be  3/5 of the distance from P to T

 

So....we  can find the partition point thusly :

 

[ x coordinate of P + (3/5) (x coordinate of T - x coordinate of P) , y coordinate of P + (3/5) (y coordinate of T - y coordinate of T )  ]   =

 

[ ( 2  + (3/5)(7  - 2)  ,  2 + (3/5)(17 - 2)) ]  =

 

[ 2  + (3/5)(5)  ,  2 + (3/5) (15)   ] = 

 

[ 2 + 3 ,  2 + 9 ]  =

 

( 5, 11)

 

cool cool cool

 Feb 18, 2020

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