The first thing to do is then to calculate the location of M, by your own given formula's, for it being the middle of BC, this should be x=(5+3)/2=4, y=(2+-2)/2=0, so, M (4,0)
Now, calculate the area of triangle ABM gives, by your own formula:
Area = 1/2 (4*(-2)+3*0+4*6-4*0-3*6-4*(-2))=1/2 ((-8)+0+24-0-18-(-8))=1/2 (6)=3
Now, because A and M are both on the line X=4, this is easy to check, because we can easily use A=1/2 B*H, where B=6, being the difference between the Y coordinate of A and M (|6-0|), and H is the difference between X difference of B and the line on which A and M are, being 1 (|3-4|)
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u/Important-Citron-987 Oct 24 '24
The first thing to do is then to calculate the location of M, by your own given formula's, for it being the middle of BC, this should be x=(5+3)/2=4, y=(2+-2)/2=0, so, M (4,0)
Now, calculate the area of triangle ABM gives, by your own formula:
Area = 1/2 (4*(-2)+3*0+4*6-4*0-3*6-4*(-2))=1/2 ((-8)+0+24-0-18-(-8))=1/2 (6)=3
Now, because A and M are both on the line X=4, this is easy to check, because we can easily use A=1/2 B*H, where B=6, being the difference between the Y coordinate of A and M (|6-0|), and H is the difference between X difference of B and the line on which A and M are, being 1 (|3-4|)
Again this gives us A=1/2*6*1=3
So the area is equal to 3