# analytic geometry

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The segment joining (-1,4), (2,-2) is extended three times its own length. Find the terminal points.

• analytic geometry -

let the end point be (x,y)

for the x-coordinate:
(x+1)/(2+1) = 3/1
x+1 =9
x = 8

for the y-coordinate:
(y-4)/(-2-4) = 3/1
y-4 = -18
y = -14
one end point is (8,-14)

we could have extended it the other way ...
(x-2)(-1-2) = 3/1
x-2 = -9
x= -7

(y+2)/(4+2) = 3/1
y+2 = 18
y = 16
in that direction the point is (-7,16)

check my arithmetic.

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