A new restaurant has ordered 64 tables for its outdoor patio. if the manager arranges the tables in a square formation, how many
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To get the midsegment, namely HN, well, we need H and N
hmm so.... notice the picture you have there, is just an "isosceles trapezoid", namely, it has two equal sides, the left and right one, namely JL and KM
the midpoint of JL is H and the midpoint of KM is N
thus
![\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) K&({{ 4q}}\quad ,&{{ 4n}})\quad % (c,d) M&({{ 4p}}\quad ,&{{ 0}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{4p+4q}{2}\quad ,\quad \cfrac{0+4n}{2} \right) \\\\\\ \left( \cfrac{2(2p+2q)}{2},\cfrac{4n}{2} \right)\implies \boxed{[(2p+2q), 2n]\impliedby N}\\\\ -----------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AK%26%28%7B%7B%204q%7D%7D%5Cquad%20%2C%26%7B%7B%204n%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0AM%26%28%7B%7B%204p%7D%7D%5Cquad%20%2C%26%7B%7B%200%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%0A%25%20%20%20coordinates%20of%20midpoint%20%0A%5Cleft%28%5Ccfrac%7B4p%2B4q%7D%7B2%7D%5Cquad%20%2C%5Cquad%20%5Ccfrac%7B0%2B4n%7D%7B2%7D%20%5Cright%29%0A%5C%5C%5C%5C%5C%5C%0A%5Cleft%28%20%5Ccfrac%7B2%282p%2B2q%29%7D%7B2%7D%2C%5Ccfrac%7B4n%7D%7B2%7D%20%5Cright%29%5Cimplies%20%5Cboxed%7B%5B%282p%2B2q%29%2C%202n%5D%5Cimpliedby%20N%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C)
hmm so.... notice the picture you have there, is just an "isosceles trapezoid", namely, it has two equal sides, the left and right one, namely JL and KM
the midpoint of JL is H and the midpoint of KM is N
thus