Let (xi, yi), i = 1, 2, 3, 4, 5, be a set of five distinct points with integer coordinates in the xy plane. show that the midpoint of the line joining at least one pair of these points has integer coordinates.

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Ответ:

hamie5124

28.01.2023

Mathematics

b. 10

Step-by-step explanation:

The distance between two points (a,b) and (c,d) is given by :_

$d=\sqrt{(d-b)^2+(c-a)^2}$

Thus, the distance between two points (10, -8) and (4, 0) is given by :_

$d=\sqrt{(0-(-8))^2+(4-10)^2}\\\\\Rightarrow\ d=\sqrt{(8)^2+(-6)^2}\\\\\Rightarrow\ d=\sqrt{64+36}\\\\\Rightarrow\ d=\sqrt{100}\\\\\Rightarrow\ d=10\text{ units}$

Hence, the distance between two points (10, -8) and (4, 0) is 10 units.

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