this problem is asking you to calculate the center of mass of a given mass distribution so in this particular problem you given the full masses and it is distributed on a plane and these are the four point masses what this kind of distribution you need to know or you need to find out what is the center of mass so in order to find it out the center of mass or this kind of distribution you need to know only the position or the coordinates of the masses the center of mass is given by x center of mass is equal to m1 m2 that's 2 plus M 3 X 3 and 4 and then you have M 1 plus M 2 this is us the average weighted average of all the masses so in order to calculate the x coordinate of the center of mass you need to know the position of the position of all the masses let's plug in the numbers here and what is M 1 and M 2 you can define M 1 and M 2 any masses and I'm just choosing this origin yes this as as my origin for the coordinate system a let's call this mass M 1 let's call this mass M 2 this mass M 3 and this matter than M 4 so you got four matters here and you can pick out which you can choose this master become 1 M 2 M 3 M 4 it depends on you so it doesn't matter how do you choose M 1 M 2 an empty you get exactly the same answer so now what is this mass let's plug in all the numbers here this mass is too clever what if they x-coordinate the x-coordinate is 0.2 meter just given here so this is point 2 m 2 now let's take a look uncle m to the mass of this M 2 is 6 below ground and the x-coordinate x-coordinate is this distance which is 2 first thing 5 meter times 5 m is right here which is kilogram and the X 3 the distance is right here because this is from the expedition this distance is 3 meter plus M for the m4 is this masked a telegram but now look at the what is the x-coordinate the x-coordinate is and the total mass M one is two plus six plus four plus eight I just need to plug in all the numbers here so once you plug in all the numbers the hands that you will get is two point three meter so this your x-coordinate of the center of mass the same way we can calculate the the center of mass or the y coordinate the y coordinate for the center of mass let's do that nobody here why senti why center of mass is given by M 1 y 1 plus M 2 y 2 M 3 y plus M 4 y 4 M 1 plus M 2 plus M 3 M 4 what's the mass M 1 the mass is 2 now here what is the y coordinate the y coordinate is what's the distance from thee in the x axis and this is the y coordinate plus M 2 m 2 8 6 mass and the y-coordinate but this is Jupiter 2 M 3 is 4 and the x coordinate the y coordinate for M 3 is you can see his 3 plus 2 is 5 same way M 4 is 8 and the y coordinate the y coordinate for this mass is 3 and the total mass is 22 plus 4 plus 8 plug in all the numbers and the answer you will get is 2 point 8 meter so your final answer is X centimeter this X center of mass white center of mass this is equal to 2 point 3 meter 2 point 8