Question

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 :).

Answer 1

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 (-2-7)) = (-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((4-3),(0+2)) = (4,0)+(3,6) = (7,6)

(3,-2) + 3((3-4),(-2-0)) = (3,-2)+(-3,-6) = (0,-8)

Answer 2

x= -5/2
y= 11/2

Answer 3

#1.
x=-4 + 5/6(5+4)=7/2
y=7 + 5/6(-2-7)=-1/2
P(7/2,-1/2)

Answer 4

#2.
x=4 + 3(4-3)=7
y=0 + 3(0+2)=6
p(7,6)
x=3 + 3(3-4)=0
y=-2 + 3(-2-0)=-8
p(0,-8)