9514 1404 393
Answer:
E = (-2, -1.5), see attached for a plot
Step-by-step explanation:
We want point E such that ...
EC/DC = 3/4 . . . . . . . . the ratio of segment lengths is 3/4
(E -C)/(D -C) = 3/4 . . . . the ratio of coordinate differences is 3/4
4(E -C) = 3(D -C) . . . . . cross multiply
4E = 3D -3C +4C . . . . isolate E term
E = (3D +C)/4 . . . . . . . divide by 4 to find E
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E = (3(-3, -4) +(1, 6))/4 = (-9+1, -12 +6)/4
E = (-2, -1.5)
The point is plotted in the attached graph.
