Why is the determinant formula giving me 0?

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Aleksander Krol
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I'm asked in a question to find out the area of quadrilateral APQR.
A(-3,1) Q(1,2) P(-4,5) R(0,6)
I used the determinant formula and i got 0.5(-6+5-24+0+18-0+8-1) = 0.5(0) = 0
but why does it give me 0? I've used this method in other questions and it worked. What am I supposed to do now?
I've found a way to calculate the area by using lengths but I find it more easier to just use the determinant formula and find out the area. :/
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mqb2766
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(Original post by Aleksander Krol)
I'm asked in a question to find out the area of quadrilateral APQR.
A(-3,1) Q(1,2) P(-4,5) R(0,6)
I used the determinant formula and i got 0.5(-6+5-24+0+18-0+8-1) = 0.5(0) = 0
but why does it give me 0? I've used this method in other questions and it worked. What am I supposed to do now?
I've found a way to calculate the area by using lengths but I find it more easier to just use the determinant formula and find out the area. :/
Can you upload the question and your work? Have you transposed the order of the points or something?
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Aleksander Krol
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(Original post by mqb2766)
Can you upload the question and your work? Have you transposed the order of the points or something?
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mqb2766
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And what was your actual working?
Note the order of points is important.

Tbh - it looks suspiciously like a square?
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Aleksander Krol
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(Original post by mqb2766)
And what was your actual working?
Note the order of points is important.

Tbh - it looks suspiciously like a square?
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Aleksander Krol
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(Original post by mqb2766)
And what was your actual working?
Note the order of points is important.

Tbh - it looks suspiciously like a square?
yeah i agree
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mqb2766
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(Original post by Aleksander Krol)
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Half understand the first row, but at best Im guessing.
Third time of mentioning it, the order of the points is important as the determinant area is signed. Im "guessing" you're summing up a positive and negative area to get zero and as the quadrilateral (square) has a lot of symmetry the signed areas have the same magnitude. This is probably because the point order jumps across a diagonal.
The order of the points in the det formula follow the order of the quadrilateral so from your picture APRQ (clockwise).
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Aleksander Krol
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(Original post by mqb2766)
Half understand the first row, but at best Im guessing.
Third time of mentioning it, the order of the points is important as the determinant area is signed. Im "guessing" you're summing up a positive and negative area to get zero and as the quadrilateral (square) has a lot of symmetry the signed areas have the same magnitude. This is probably because the point order jumps across a diagonal.
The order of the points in the det formula follow the order of the quadrilateral so from your picture APRQ (clockwise).
omg yesssss it worked!!! i got 17 units^2 thanks!!!!! <3
so should we always write the points in the determinant formula in clockwise?
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mqb2766
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(Original post by Aleksander Krol)
omg yesssss it worked!!! i got 17 units^2 thanks!!!!! <3
so should we always write the points in the determinant formula in clockwise?
Why not try anti clockwise?
Then choose an order, as per the OP, which jumps along one diagonal say.
What do you get in each case / why?

Note - Im guessing the model solution would expect you to simply conclude its a square so 4^2+1^2 = ... Its a lot simpler.
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Aleksander Krol
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(Original post by mqb2766)
Why not try anti clockwise?
Then choose an order, as per the OP, which jumps along one diagonal say.
What do you get in each case / why?

Note - Im guessing the model solution would expect you to simply conclude its a square so 4^2+1^2 = ... Its a lot simpler.
thanks again btw!! i really do appreciate for helping me out!! :"))
i found the det formula more efficient, cause all i have to do, is just write the points and multiply then add and subtract, and then finally halve it.
but yeah you're right, ig they wanted us to simply conclude that it's a square.
also i'm not sure, but i think the reason i got 0 at first when i used the det formula instead of going clockwise or anticlockwise, is maybe because since the lengths are same in a square, so when i subtracted, they cancelled out, which is why i got 0. but yeah i maybe wrong.
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mqb2766
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(Original post by Aleksander Krol)
thanks again btw!! i really do appreciate for helping me out!! :"))
i found the det formula more efficient, cause all i have to do, is just write the points and multiply then add and subtract, and then finally halve it.
but yeah you're right, ig they wanted us to simply conclude that it's a square.
also i'm not sure, but i think the reason i got 0 at first when i used the det formula instead of going clockwise or anticlockwise, is maybe because since the lengths are same in a square, so when i subtracted, they cancelled out, which is why i got 0. but yeah i maybe wrong.
There is a reasonable description about using determinants for triangles/quadrilaterals
https://www.nagwa.com/en/explainers/890151902620/
Its up to you what method you use to answer problems, but I guess in this case you don't really understand the assumptions in deriving the determinant formula applied to areas, so applied it incorrectly.

While I could try and reverse engineer which points were paired up in your det formula in #5, Id suggest it would be beneficial if you were clearer in the first place (an examiner may give you zero marks as its not clear what you're trying to do or where your mistake is) and you tried to understand what you did using the previous link. That way, you'd better understand the assumptions made and youd make fewer mistakes in future. If you have progress/problems in doing that, just post what you've done.

Tbh, I'd just remember the picture of putting a bounding rectangle around a triangle or quadrilateral, and if necessary rederive the formula from the picture. Its simply: bounding rectangle subtract each x-y right angled triangle (assuming convex). However, get in the habit of using the method appropriate for the question. Here, its simply the area of a square. Anything else will waste time / introduce the potential for errors.
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Aleksander Krol
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(Original post by mqb2766)
There is a reasonable description about using determinants for triangles/quadrilaterals
https://www.nagwa.com/en/explainers/890151902620/
Its up to you what method you use to answer problems, but I guess in this case you don't really understand the assumptions in deriving the determinant formula applied to areas, so applied it incorrectly.

While I could try and reverse engineer which points were paired up in your det formula in #5, Id suggest it would be beneficial if you were clearer in the first place (an examiner may give you zero marks as its not clear what you're trying to do or where your mistake is) and you tried to understand what you did using the previous link. That way, you'd better understand the assumptions made and youd make fewer mistakes in future. If you have progress/problems in doing that, just post what you've done.

Tbh, I'd just remember the picture of putting a bounding rectangle around a triangle or quadrilateral, and if necessary rederive the formula from the picture. Its simply: bounding rectangle subtract each x-y right angled triangle (assuming convex). However, get in the habit of using the method appropriate for the question. Here, its simply the area of a square. Anything else will waste time / introduce the potential for errors.
i found the link quite helpful!! i think i do understand it now.
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