Question

find the distance d(p1,p2) between the points p1 and p2. p1=(a,r) p2=(0,0) d(p1,p2)= (simplify your answer. type an exact answer, using radicals as needed)

Explanation:

Step1: Recall distance formula

The distance formula between two points $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ is $d(P_1,P_2)=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1 = a,y_1=r,x_2 = 0,y_2 = 0$.

Step2: Substitute values

Substitute the values into the formula: $d(P_1,P_2)=\sqrt{(0 - a)^2+(0 - r)^2}=\sqrt{(-a)^2+(-r)^2}$.

Step3: Simplify

Since $(-a)^2=a^2$ and $(-r)^2=r^2$, we get $d(P_1,P_2)=\sqrt{a^2 + r^2}$.

Answer:

$\sqrt{a^2 + r^2}$