To determine the distance between two points in the cartesian plane, we use the Pythagorean theorem to calculate it from the coordinates of them, as follows:
[tex]d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
To solve it we will substitute the given values, as follows:
[tex]d=\sqrt[]{(2\frac{1}{5}-2\frac{1}{5})^2+(-3\frac{1}{4}-(-6\frac{3}{4}))^2}[/tex][tex]d=\sqrt[]{(0)^2+(6\frac{3}{4}-3\frac{1}{4})^2}[/tex][tex]d=\sqrt[]{((6-3)\frac{(3-1)}{4})^2}[/tex][tex]d=\sqrt[]{(3\frac{2}{4})^2}[/tex][tex]d=3\frac{2}{4}[/tex]
If we simplify the fraction, we find the following:
[tex]d=3\frac{1}{2}[/tex]
