Given:
Two points are (-1,10) and (-5,3).
Required:
Find the distance between the given points.
Explanation:
The distance between two points is given by the formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]consider
[tex](x_1,y_1)=(-1,10)\text{ and \lparen x}_2,y_2)=(-5,3)[/tex]The distance between the given points is:
[tex]\begin{gathered} d=\sqrt{(-5-(-1))^2+\left(3-10\right)^2} \\ d=\sqrt{(-5+1)^2+(-7)^2} \\ d=\sqrt{(-4)^2+49} \\ d=\sqrt{16+49} \\ d=\sqrt{65} \end{gathered}[/tex]Final Answer:
The distance between the given points is
[tex]\sqrt{65}[/tex]