topscore test 2 qr #14

[TimeforDAT]

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find the area of a triangle given three coordinates (3,-6), (1,1), (7,6). They show some weird formula in the solutions. Can someone explain what that formula is using the x1, x2, x3, y1, y2, y3. I know where that 1/2 comes into play, but not the rest of it.


thanks!

 

[Lonely Sol]

find the area of a triangle given three coordinates (3,-6), (1,1), (7,6). They show some weird formula in the solutions. Can someone explain what that formula is using the x1, x2, x3, y1, y2, y3. I know where that 1/2 comes into play, but not the rest of it.


thanks!

This question is answered by Streetwolf like 100 times already! But here is what he basically said,

The easiest way to do this problem is to set up matrices. Whenever you are given anything else but a triangle, I am sure this way will work!

First, get one of the side to the origin, lets pick (1,1), we need to substract 1 from x-axis and 1 from y-axis to get it to origin. Therefore we substract 1 from both of the other coordinates

You should end up with (0,0) (2,-7) (6,5)

Now, use (a*d)-(b*c) = (2*5)-(-7*6) = 52

Then divide 54 by 2; 52/2 = 26

 

[Streetwolf]

This question is answered by Streetwolf like 100 times already! But here is what he basically said,

The easiest way to do this problem is to set up matrices. Whenever you are given anything else but a triangle, I am sure this way will work!

First, get one of the side to the origin, lets pick (1,1), we need to substract 1 from x-axis and 1 from y-axis to get it to origin. Therefore we substract 1 from both of the other coordinates

You should end up with (0,0) (2,-7) (6,5)

Now, use (a*d)-(b*c) = (2*6)-(-7*6) = 54

Then divide 54 by 2; 54/2 = 27

Should be 2*5 and you get 52/2 = 26, otherwise it's fine.

 

[EngDentist]

You could also use:
Area = 1/2|[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]|

Using this formula, I get the area as 26.

 

[Vapor1122]

I just drew it as close to scale as possible and estimated. IIRC, I was off by one.

 

[TimeforDAT]

This question is answered by Streetwolf like 100 times already! But here is what he basically said,

The easiest way to do this problem is to set up matrices. Whenever you are given anything else but a triangle, I am sure this way will work!

First, get one of the side to the origin, lets pick (1,1), we need to substract 1 from x-axis and 1 from y-axis to get it to origin. Therefore we substract 1 from both of the other coordinates

You should end up with (0,0) (2,-7) (6,5)

Now, use (a*d)-(b*c) = (2*5)-(-7*6) = 52

Then divide 54 by 2; 52/2 = 26

oh ok i see now thank you

 

[theun4given]

Now, use (a*d)-(b*c) = (2*5)-(-7*6) = 52

26

where does this formula come from?

 

[Streetwolf]

Determinant.