Question

Find the distance between the points given.

(0, -6) and (9, 6)

Answer 1

AB=9
AC=`12
BC=x=?
ABC is a triangle with 90 degree
x2=(9)2+(12)2
x2=81+144
x2=225
x=15 so the distance between the points given is 15

Answer 2

$A(x_1;\ y_1);\ B(x_2;\ y_2)\\\\The\ distance\ between\ A\ and\ B:\\|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\-------------------------\\(0;-6)\to x_1=0\ and\ y_1=-6\\(9;\ 6)\to x_2=9\ and\ y_2=6\\\\d=\sqrt{(9-0)^2+(6-(-6))^2}=\sqrt{9^2+12^2}=\sqrt{81+144}\\=\sqrt{225}=15\\\\Answer:\boxed{15}$