SOLUTION: Point A is located at (4,1) and point B is located at (9,13). What are the coordinates of the point that partitions the directed line segment AB in a 4:1 ratio?

Question 1064983: Point A is located at (4,1) and point B is located at (9,13).
What are the coordinates of the point that partitions the directed line segment AB in a 4:1 ratio?
Found 3 solutions by Boreal, josgarithmetic, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
The x coordinate is 4/5 of the way from 4 to 9, and that distance is 5, so the x coordinate is at 8.
The y coordinate is 4/5 of the way from 1 to 13, and that distance is 12, so the y coordinate is 48/5 or 9.6 of the way or at 10.6
(8,10.6) is the coordinate.
Distance from A is sqrt ((8-4)^2+(10.6-1)^2)= sqrt (16+92.16)=sqrt (108.16)=10.4 units
Distance from B is sqrt ((9-8)^2+(13-10.6)^2=sqrt(1+5.76)=sqrt(6.76)=2.6 units
Total distance is sqrt (12^2+5^2)=13
10.4 is 4/5 of the way to 13.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Point A is located at (4,1) and point B is located at (9,13).
What are the coordinates of the point that partitions the directed line segment AB in a 4:1 ratio?

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