Analytic Geometry
posted by Amber .
Please help. I've been trying to solve these for more than an hour now but I can't seem to get it.
1) The segment joining (4,7), (5,2) is divided into two segments, one of which is 5 times as long as the other. Find the point of division.
2) The segment joining (4,0), (3, 2) is extended each way a distance equal to three times its own length. Find the terminal points.
Please show the solutions so I can study them. Thanks in advance :).

1)
Naturally, there are two places to make the division: one near (4,7) and the other near (5,2)
Taking the one near (4,7), we want a point which is 1/6 the way to (5,2).
(4 + 1/6 (5+4),7 + 1/6 (27)) = (5/2,11/2)
2)
in the same way as above, figure the difference between the points and go out 3 times that distance in each direction:
(4,0) + 3((43),(0+2)) = (4,0)+(3,6) = (7,6)
(3,2) + 3((34),(20)) = (3,2)+(3,6) = (0,8) 
x= 5/2
y= 11/2 
#1.
x=4 + 5/6(5+4)=7/2
y=7 + 5/6(27)=1/2
P(7/2,1/2) 
#2.
x=4 + 3(43)=7
y=0 + 3(0+2)=6
p(7,6)
x=3 + 3(34)=0
y=2 + 3(20)=8
p(0,8)
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