SOLUTION: Point Y(6,4) partitions segment XZ in the ratio 3:1. The coordinates of X are (-3,-2). Find the coordinates of Z.

Question 1180598: Point Y(6,4) partitions segment XZ in the ratio 3:1. The coordinates of X are (-3,-2). Find the coordinates of Z.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
(-3, -2) to (6,4) is a change in X of +9 and Y of +6. That is 3 times the change from Y to Z, which would have to be +3 for X and +2 for Y, making Z (9, 6).
this can be checked.
Distance of X to Y is sqrt (diff x^2+diff y^2)=sqrt (81+36)=sqrt (117)=3 sqrt(13)
YZ would be 1/3 of that or sqrt (13).
This would require z to have an x-value of 3 more (absolute value) and a y-value of 2 more (absolute value), or (9, 6)
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distance from y to z is sqrt(13)
from x to z is sqrt (144+64)=sqrt(208), or 4 sqrt (13).

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