Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
1 answer:
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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