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I have to "show" that the mid point co-ordinate of a line segment given by (x1,y1) and (x2,y2) is equal to ([x1+x2]/2,[y1+y2]/2). My solution I thought was quite simple:

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I have "shown" that x2 is the mid point between x1 and x3 and that this can by calculated by [xi + xj]/2, and this clearly can apply to the y dimension also.

Now, for the real mathematicians solution, this question comes from Morris Kline's "Calculus an intuitive approach", solution is based on figure from this book.

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So my original question was why does 3 points in the y dimension being parallel, given 1 point cuts the traversal in half, mean the traversal in the x dimension is cut in half?

Second question is what the hell is going on with the analysis of [(x2-x1)/2] + x1 = (x1+x2)/2?

Also, how can y3 be the median of the trapezoid? In what way are we referring to the middle number?

Cheers!

OpenSauce
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    Your proof is incorrect, because you haven't shown that $\left(\frac{x_1+x_2}2,\frac{y_1+y_21}2\right)$ is on the same line as $(x_1,y_1)$ and $(x_2,y_2)$, nor that it is the same distance from both of them. – saulspatz May 17 '21 at 13:12
  • I used your comment to generate a similar proof to the answer above, therefore I now am more confident in my new proof (Using the isosceles triangle, not isosceles trapezoid) , which I may add here when I have the time. Thank you. – OpenSauce May 28 '21 at 12:36

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