 Then what we've got to do is Actually, let's leave this guy here So this becomes the distance of O M right Now what we've got to do is Find the distance of we've got this guy find the distance of a m Okay, so what we do we go back here. We say this is now distance of a m Distance of a m is going to be this point to this point So we already marked that one as our second coordinate We're going to take the one off this guy. I'm going to put it on this That's going to be our first coordinate So again, we're going to go through this formula x2 minus x1 which is going to be x over 2 minus or x1 is 0 square plus y over 2 Minus a wise 2 minus y1 now y2 is y over 2 minus y Square so over here, we got x over 2 minus 0 is just x over 2 so we've got x over 2 square plus How do you subtract these guys you do these by common denominator, right? You should be looking back at your fractions if you don't remember this whenever you have a variable by itself It just means it's over 1 so the common denominator between these is 2 What did you multiply 2 by to give you 2 you multiply by 1 so that guy just remains y You multiply 1 by 2 so you got to multiply the top by 2 as well So 2 times y is minus 2 y squared So let's take this one more level. We got x squared over 2 that just becomes x squared over 4 and then we got plus y minus 2 y is negative y So this guy becomes negative y over 2 Square, are you still going to be able to see this you are That's good so That's going to stay what it is y squared over 4 plus negative y squared is y squared Over 2 squared is going to be 4 So right now you're still on the board who are still on the board So these guys have the same common denominator. So it's going to be x squared plus y squared over 4 And as we talked about earlier for that guy for the distance of om You can separate the top from the bottom and take the square root of the bottom and the square root of the top The top you can't break down because the plus sign attaches up. So this becomes equals the square root of x squared plus y squared And the square root of 4 is just 2 so that becomes 2 we're on the board. We're on the board So the distance of am is Distance of am is equal to square root of x squared plus y squared over 2 Which is the distance of 1 so we just went ahead And proved this guy now this question would Be a grade 11 easy grade 11 question or a hard grade 10 question in north america specifically anyway So it's two dimensional proof using coordinate systems And in the question we used the midpoint Formula and the distance formula And that's basically it. That's all we ended up using to go through this proof