Question

find the distance ( d(p_1,p_2) ) between the given points ( p_1 ) and ( p_2 ).
( p_1 = (1,0) )
( p_2 = (5,3) )
( d(p_1,p_2) = square )
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

Given \(P_1=(0,0)\) and \(P_2=(2,5)\).

Step2: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute \(x_1 = 0,y_1 = 0,x_2 = 2,y_2 = 5\) into the formula:
\(d=\sqrt{(2 - 0)^2+(5 - 0)^2}=\sqrt{2^2 + 5^2}\).

Step3: Calculate the squares

\(2^2=4\) and \(5^2 = 25\). So \(d=\sqrt{4 + 25}\).

Step4: Sum and simplify

\(4+25 = 29\), so \(d=\sqrt{29}\).

Answer:

\(\sqrt{29}\)