Respuesta :
Answer:
(a)3√13 Units
(b)
[tex](\frac{5\sqrt{5}}{2},-2\sqrt{2})[/tex]Explanation:
Part A
We determine the distance between the two points using the distance formula.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, the distance between points (√5, √2) and (4√5, -5√2) is:
[tex]\begin{gathered} =\sqrt{(4\sqrt{5}-\sqrt{5})^2+(-5\sqrt{2}-\sqrt{2})^2} \\ =\sqrt{(3\sqrt{5})^2+(-6\sqrt{2})^2} \\ =\sqrt{(3^2\times5)+((-6)^2\times2)} \\ =\sqrt{45+72} \\ =\sqrt{117} \\ =3\sqrt{13}\text{ Units} \end{gathered}[/tex]The exact distance between the points is 3√13 Units.
Part B
We determine the midpoint of the line segment whose endpoints are the given points using the midpoint formula.
[tex]\text{Midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Therefore:
[tex]\begin{gathered} \text{Midpoint}=(\frac{\sqrt{5}+4\sqrt{5}}{2},\frac{\sqrt{2}+(-5\sqrt{2})}{2}) \\ =(\frac{5\sqrt{5}}{2},\frac{-4\sqrt{2})}{2}) \\ =(\frac{5\sqrt{5}}{2},-2\sqrt{2}) \end{gathered}[/tex]