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

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?

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Dave D. | Math and Physics TutorMath and Physics Tutor
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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)