In the xy-coordinate plane, point P has a coordinates (6,2) Point Q has coordinate (18,8).

Question

If Point x is on segment PQ so that the length of segment PX is twice the length of segment XQ what are the coordinates of point x?

Answer 1

 

 

For the conditions stated, if one line segment (PX) is twice the length of the other (XQ), then point X must be 2/3 of the way towards Q because let s = the length of XQ and 2s = length of PX

2s / (2s +s) = 2s / 3s  = 2/3

 

Therefore, if we go 2/3 the distance in the x direction from point P and 2/3 the distance in the y direction from point P, we will arrive at the location for point X. 

 

So this turns out to be

(2/3) × (18-6) = 8 in the X direction 

 

AND

 

(2/3) × (8-2) = 4 in the Y direction 

 

And our final answer is :

 

(X,Y) = (6+8, 2+4) = (14, 6)