SOLVE

Let's admit you're right, prove me i'm wrong.

OP HERE:
that's not how it works. You don't have to prove a contention wrong... the onus is on the claimant to do the proving.

Nevertheless, I'm not arguing your answer... I'm just looking for a more detailed proof as to why "moving the central point doesn't change the sum of opposites area". And "moving the point and checking the area again" isn't a proof, it's just brute force. I'm looking for some reasoning why it works.

Look out guys, looks like we got Tholians again...

It's either boring homework threads like this or pseudoscience /x/ threads. Can't have both

I don't get it.

That only holds if you're one translation away from the dot being in the centre.

Fuck, I finally solved it
If I don't have a numerical error, it indeed is 20

An easy way to know if the total area changed is to compute the added area and the substracted area when you move the point, these two are equal, which mean the area didn't changed

But why?

it's kinda long to type out but divide the square to 4 squares in the middle and form triangles with the edges currently there
form there on you can write some relations to help you calculate since neighboring triangles will have the same area