February 13th, 2018, 08:37 AM  #1 
Newbie Joined: Feb 2018 From: Iran Posts: 16 Thanks: 3  Analytic of point
If the area of triangle ABC with the vertices A(3,1) B(1,2) and C(m,1) is five square units find the possible values of m?

February 13th, 2018, 09:51 AM  #2 
Newbie Joined: Dec 2017 From: Spain Posts: 15 Thanks: 1 
Drawing that in a coordinatesystem, you might notice that the point C has to lie on the function f(x)=1. The altitude to the side AC equals 3 units (=1(2)). Hence (using area formula: h(c)*c/2) we get: 5=c*3/2 $\ \ \ \ \ \ \ $ /*(2/3) 10/3=c Now, remember that the triangle ABC can also be obtuse. Thus the point C lies on (19/31) or (1/31). (You either subtract 10/3 from 3 or add it). We finally have: m(1)=19/3≈6,3 m(2)=1/3≈0,3 Last edited by skipjack; February 13th, 2018 at 05:28 PM. 

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