SOLUTION: The segment joining (-3,-2) and (-1/2,3) is extended a distance equal to 4/5 of its own length. Find the terminal point.

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Question 981832: The segment joining (-3,-2) and (-1/2,3) is extended a distance equal to 4/5 of its own length. Find the terminal point.
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
Label (-3,-2) A, (-1/2, 3) B and Terminal point T.
Distance between A and B = 5
Distance between B and T = 4
AB/BT = 5/4
b - a/t - b = 5/4
Cross multiply
5(t - b) = 4(b - a)
5t - 5b = 4b - 4a
Collect like terms
5t = 4b - 4a + 5b
5t = 9b - 4a
T = 1/5(9b - 4a)
T = 1/5( 9(-1/2,3)) - 4(-3 -2))
T = 1/5(-9/2 , 27) + (12 ,8)
T = 1/5(15/2, 35)
T = (3/2,7)
This is the Terminal point.
Hope this helps :-)