What is the perimeter of a triangle with corners at #(3 ,4 )#, #(6 ,7 )#, and #(4 ,5 )#?

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Answer 1 · 2018-06-02T13:44:31

#color(blue)("No triangle exists")#

Labelling the points:

#A=(3,4), B=(6,7), C=(4,5)#

Vectors:

#vec(AB)=((3),(3))#

#vec(AC)=((1),(1))#

#vec(AC)=mu((3),(3))color(white)(888888)#, for #mu=1/3#

#:.#

#vec(AC)=1/3vec(AB)#

This means the points are collinear ( all lying on a straight line ), so these points do not form a triangle.