Question

find the distance d (p₁,p₂) between the points p₁ and p₂. p₁ = (k,t) 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 $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given points

Substitute $x_1=k, y_1=t, x_2=0, y_2=0$:
$d(P_1,P_2)=\sqrt{(0-k)^2+(0-t)^2}$

Step3: Simplify the expression

Simplify the squared terms:
$\sqrt{(-k)^2+(-t)^2}=\sqrt{k^2+t^2}$

Answer:

$\sqrt{k^2+t^2}$