What is the coordinates of point P ?

Given a straight line passes through the points #M(10,13)# and #N(4,-2)#. A point P divides the line segmen #MN# such that #2MN=3MP#. Find the coordinates of point P

1 Answer
Jim G.
Sep 4, 2017

#P=(6,3)#

Explanation:

#"taking a vector approach to the question"#

#2vec(MN)=3vec(MP)#

#rArr2(uln-ulm)=3(ulp-ulm)#

#rArr2uln-2ulm=3ulp-3ulm#

#rArr3ulp=2uln+ulm#

#color(white)(rArr3ulp)=2((4),(-2))+((10),(13))#

#color(white)(rArr3ulp)=((8),(-4))+((10),(13))=((18),(9))#

#rArrulp=1/3((18),(9))=((6),(3))#

#rArrP=(6,3)#

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