+118659 Hi Guest,
CPhill (Chris) asked me to take a look at this question. The answer is not obvious to either of us, I am sure there is an easy way to do it but that it not the way I do things LOL
Chris asked me if I could draw a picture because niether us us were convinced that there was one single answer.
The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. Find the length of the median of the trapezoid.
One of the problems here is that trapezoid has different meanings in different countries but I have taken a trapezoid to be a quadrilateral with 2 parallel sides. (In Australia we call this a trapezium)
I have drawn it using desmos graphing calculator
The diagonals are in red. I have fixed the 8 unit diagonal and allowed the 10unit diagonal to take different positions.
This is the movable graph:
https://www.desmos.com/calculator/hyyc21q968
You can move the slider b to see all the different possible trapeziums that can be formed.
The black line is the median (half way between the two parallel lines.)
When you slide the b slider you can see that althought the trapezium changes shape the median appears to stay the same length.
I ran the distance formula though Wolfram|Alpha it says the distance of the median is always 6.40312 units
Wolfram Alpha calculation of the length
I have not shown you all my calculations although some are displayed in the Desmos formula list.
Anyway, like I said, I am sure there is a much easier way to get the answer. ://
Here is a pic but it is much better to look at the adjustable version in the link above.
