strategy guide geomtry #10 p71

[gmatxyz]

if the coordinates A (-5,6) and B (-2,0)..whats the coordinate 3x as far from A then B...the answer is (-2.75,1.5)

but why doesn't the "midpoint" formula work but divide by 4 instead of 2? so id add (-5+-2)/ 4..and (6+0)/4...as you can see it works only for the y coordinate. conceptually why doesn't it work for the x coordinate?

[RonPurewal]

if you're going to do that, you need to do (x + 3y)/4. this would be a 'weighted' average, with three times as much 'weight' on the coordinates of B (the closer point).

(your formula doesn't 'work' with the y-coordinates; you just got lucky, since three times 0 is still 0.)