Respuesta :
Given the points
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(2,\frac{5}{2}) \\ (x_2,y_2)\Rightarrow(\frac{8}{3},1) \end{gathered}[/tex]To find the distance, d, between the two points,
The formula is
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute the values into the formula of the distance between two points above
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(\frac{8}{3}-2)^2+(1-\frac{5}{2})^2} \end{gathered}[/tex]Solve to find d,
[tex]\begin{gathered} d=\sqrt[]{(\frac{8}{3}-2)^2+(1-\frac{5}{2})^2} \\ d=\sqrt[]{(\frac{2}{3})^2+(-\frac{3}{2})^2} \\ d=\sqrt[]{\frac{4}{9}+\frac{9}{4}} \\ d=\sqrt[]{\frac{97}{36}}=\frac{\sqrt[]{97}}{6} \\ d=\frac{\sqrt[]{97}}{6}=1.64\text{ (two decimal places)} \\ d=1.64\text{ (two decimal places)} \end{gathered}[/tex]Hence, the simplest radical form of the distance, d, between the two given points is 1.64 ( two decimal places).
