Question

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?

Answer 1

E = (1, 2)

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)