SOLUTION AND EXPLANATION
The distance between two-point A and B is given as
![|AB|=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}](https://img.qammunity.org/2023/formulas/mathematics/college/qjplvjpgibufxhn6uyn4ny1gbalxw7enun.png)
From the diagram in the question the two-point given are

Where

Substitute the parameters into the formula above
![\begin{gathered} |AB|=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ |AB|=\sqrt[]{(6-3)^2+(6-1)^2} \\ |AB|=\sqrt[]{3^2+5^2} \\ |AB|=\sqrt[]{9+25} \\ |AB|=\sqrt[]{34} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/4r1fibua79m3es1u1z5wyi6qmavlkxesna.png)
Hence, the distance between the two points is

Therefore the distance between the two-point is 5.8unit to the nearest tenth
The Third option is correct