SOLUTION: Hey there, thanks its veery urgent question haveing trouble could u please answer with a diagram if possible!! the question is :FInd the area of triangle whose vertices are A(4,-2

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Question 203869: Hey there, thanks its veery urgent question haveing trouble could u please answer with a diagram if possible!!
the question is :FInd the area of triangle whose vertices are A(4,-2)B(-6,4)C (8,-2)
thanks soo much appriciate it!!
Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!


To begin with, let us see the triangle,
drawing%28400%2C400%2C-10%2C10%2C-5%2C6%2Cgrid%281%29%2Cgraph%28400%2C400%2C-10%2C10%2C-5%2C6%29%2Ctriangle%284%2C-2%2C-6%2C4%2C8%2C-2%29%2C+red%28locate%283.5%2C-2.15%2CA%29%29%2Cred%28locate%28-6.5%2C4.55%2CB%29%29%2Cred%28locate%288.2%2C-2.15%2CC%29%29%29---> Obtuse Triangle

We know finding Area for Triangle, A=%281%2F2%29bh, Working Eqn.

In the given Obtuse Triangle, the perpendicular Height lies outside.
drawing%28400%2C400%2C-10%2C10%2C-5%2C6%2Cgraph%28400%2C400%2C-10%2C10%2C-5%2C6%29%2Ctriangle%284%2C-2%2C-6%2C4%2C8%2C-2%29%2C+red%28locate%283.5%2C-2.15%2CA%29%29%2Cred%28locate%28-6.5%2C4.55%2CB%29%29%2Cred%28locate%288.2%2C-2.15%2CC%29%29%2Cgreen%28line%28-6%2C-2%2C-6%2C4%29%29%2Cgreen%28locate%28-6.5%2C-2.15%2CD%29%29%2Cred%28locate%28-8.5%2C2%2Cheight%29%29%2Cgreen%28line%28-6%2C-2%2C4%2C-2%29%29%2Cred%28line%284%2C-2%2C8%2C-2%29%29%2Cred%28locate%285.5%2C-2.15%2Cbase%29%29%2Cred%28locate%28-5.7%2C-1.2%2C90%5Eo%29%29%29

To find height, we take distance between points "B" & "D"
by taking their coordinates.

Applying Distance Formula = h=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29%29
h=sqrt%28%28-6-%28-6%29%29%5E2%2B%28-2-4%29%5E2%29
h=sqrt%28%28-6%2B6%29%5E2%2B%28-6%29%5E2%29=sqrt%280%2B36%29=sqrt%2836%29
red%28h=6units%29

Finding for the base, we use the same Distance Formula between points "A" & "C",
b=sqrt%28%288-4%29%5E2%2B%28-2-%28-2%29%29%5E2%29
b=sqrt%284%5E2%2B0%5E2%29=sqrt%2816%29
red%28b=4units%29

Therefore, going back to our Working Eqn,
A=%281%2F2%29bh=%281%2F2%29%284%29%286%29=24%2F2
red%28A=12square_units%29, Answer

Thank you,
Jojo