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about analytic geometry: the line segment joining the points (-2, -1) and (6, 4) is divided into two segments, one of which is three times as long as the other. find the point of division(note: Give two possible answers.) please show your solution. thanks in advance :)

Sagot :

Given the full segment endpoints (-2, -1) and (6,4)
(Please click image for the illustration and solution.)

After dividing the full segment into two segments where the longer segment is three times the shorter segment:

The possible division points are:
A.  (0, 1/4)
The endpoints of the segments are:
Shorter segment:  (-2,-1) and (0, 1/4)
Longer segment:  (0, 1/4) and (6,4)

B.  (4, 11/4)
The endpoints of the segments are:
Shorter segment:  (4, 11/4) and ( 6, 4)
Longer segment:  ( -2, -1) and (4, 11/4) 

(PLEASE CLICK IMAGE BELOW FOR SOLUTION with ILLUSTRATION)

Note: I included the solution for lengths of the segments :-) 


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