ANSWER
d = 13
EXPLANATION
We want find the distance between two points N(-5, -15) and P(-5, -2).
To do this, we will use the formula below:
[tex]d\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]We have that:
x1 = -5
x2 = -5
y1 = -15
y2 = -2
Therefore:
[tex]\begin{gathered} d\text{ = }\sqrt{(-5-(-5))^2+(-2-(-15))^2} \\ d\text{ = }\sqrt{(-5+5)^2+(-2+15)^2} \\ d\text{ = }\sqrt{0+(13)^2} \\ d\text{ = }\sqrt{13^2} \\ \Rightarrow\text{ d = 13} \end{gathered}[/tex]