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February 13th, 2018, 08:37 AM   #1
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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?
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February 13th, 2018, 09:51 AM   #2
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Drawing that in a coordinate-system, 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 (19/3|1) or (-1/3|1). (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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