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Circle equations — Basic example

Video transcript

a circle in the XY plane has a diameter with endpoints at 8 comma 10 and negative 2 comma 0 which of the following is the center of the circle so let's think about it if you have if you have some circle in the XY plane so this is my best attempt at drawing a circle and if it had if you had two end points of a diameter so let's say let's say that this is let's say that this is a diameter right over here it looks something like it looks something like this so let's say that's our diameter right over there and if this point was the point negative 2 comma 0 and this was the point 8 comma 10 what would be the coordinates of the center of the circle well the coordinates of the said the centre of the circle is going to be the midpoint of these two endpoints of a diameter in fact the center of a circle is always going to be the midpoint of the two endpoints of the center of a diameter if the diameter was this right over here if the diameter was this over here then once again the center of the circle is the midpoint of that point in that point right over there so to answer this question always have to find the midpoint of this point and this point right over there and to find a midpoint we just have to find the average of the x-coordinates and the average of the y-coordinates so let's see this is going to be 8 the x-coordinate the the average of 8 and negative 2 is 8 plus negative 2 plus negative 2 over 2 and the average of 10 and 0 and we know that's 5 but we could say that's 10 plus a 0 over 2 now let's see 8 plus negative 2 is 6 divided by 2 is 3 and then 10 divided by 2 is 5 3 comma 5 and we see it right over there