Question

find the distance d (p₁,p₂) between the given points p₁ and p₂. p₁ = (0,0) p₂ = (1,2) 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: Identify coordinates

Here, \(x_1 = 0,y_1 = 0,x_2 = 1,y_2 = 2\).

Step3: Substitute into formula

\(d=\sqrt{(1 - 0)^2+(2 - 0)^2}=\sqrt{1^2 + 2^2}=\sqrt{1 + 4}=\sqrt{5}\).

Answer:

\(\sqrt{5}\)