Question

Find the distance between (-5,3) and (-6,6).

Answer 1

`\begin{gathered} \text{let (x}_1,y_1)=(-5,3)\text{ and (x}_2,y_2)=(-6,6) \\ \text{the distance is given by} \\ d=\sqrt[]{\text{(x}_2-\text{x}_1)^2+(y_2}-y_1)^2 \\ \text{hence, one has} \\ d=\sqrt[]{(-6-\mleft(-5\mright))^2+\mleft(6-3\mright)}^2 \\ d=\sqrt[]{(-6+5)^2+(3)}^2 \\ d=\sqrt[]{(-1)^2+9} \\ d=\sqrt[]{1+9} \\ d=\sqrt[]{10} \end{gathered}`