Points g, e, and o are collinear on segment go, and ge: eo = 3: 4. g is located at (-5,-1), o is located at (9,6). what are the coordinates of point e?

  E = (1, 2)

Step-by-step explanation:

You want ...

  (E -G) : (O -E) = 3 : 4

  4(E -G) = 3(O -E) . . . . . . . . "cross multiply"

  4E -4G = 3O -3E . . . . . . . . eliminate parentheses

  7E = 4G + 3O . . . . . . . . . . . add 3E+4G

  E = (4G +3O)/7 . . . . . . . . . .divide by 7

  E = (4(-5, -1) +3(9, 6))/7 = (-20+27, -4+18)/7 = (7, 14)/7 . . . . fill in G and O

  E = (1, 2)