The formula to find the distance between two points with coordinates (x₁,y₁) and (x₂,y₂) is:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute x₁=-5, x₂=-5, y₁=-15 and y₂=-2 to find the distance between the given points:
[tex]\begin{gathered} d=\sqrt[]{((-5)-(-5))^2+((-15)-(-2))^2} \\ =\sqrt[]{(-5+5)^2+(-15+2)^2} \\ =\sqrt[]{(0)^2+(-13)^2} \\ =\sqrt[]{0+169} \\ =\sqrt[]{169} \\ =13 \end{gathered}[/tex]Therefore, the distance between the points N and P is:
[tex]13[/tex]