Point Y partitions XZ with coordinates X (-1, 5) and Z (11, -3) such that XY: YZ is 3:1. What are the coordinates of Y?

Find the coordinates of point Y if Y is between X and Z, X = (-1,5) and Z = (11,-3) such that XY:YZ = 3:1

 

Since the ratio is 3 to 1, the point Y must be three-fourths of the way from (-1,5) to (11,-3).

 

From -1 to 11 is 12 units, three-fourths of 12 is 9 and 9 steps from -1 to 11 get you to 8.

 

From 5 to -3 is 8 units, three-fourths of 8 is 6 and 6 steps from 5 to -3 get you to -1.

 

The point is (8,-1).

 

I wrote this so Y is between X and Z. It doesn't have to be; the line segment could be YXZ or XZY.

 

I you want the other answers, you will need to re-post.