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## anonymous one year ago A classmate tells you "Finding the coordinates of the midpoint is easy. You must just find the averages." Is there any truth to it? Explain what you think your classmate means.

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1. anonymous

yes, that's true. the coordinates of the midpoint is the average of the coordinates of the endpoints. If $$(x_1,y_1)$$ and $$(x_2,y_2)$$ are endpoints, the midpoint is $\left( \frac{ x_1+x_2 }{ 2 },\frac{ y_1+y_2 }{ 2 } \right)$

2. MrNood

|dw:1442349870817:dw| it can be seen that the midpoint is the 'middle' of both the x and y lines now: the length of the Y dotted line is x2-x1 and the length of half of this is therefore (x2-x1) / 2 but you need to add the start point to this to get the actual midpoint so midpoint = (x2-x1)/2 + x1 and that is the same as (x1+x2)/2 which is the same as the average of x1 and x2 same for Y

3. MrNood

CORRECTION above "the length of the Y dotted line is x2-x1" should be "the length of the X dotted line is x2-x1"

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