Question

find the distance ( d(p_1,p_2) ) between the given points ( p_1 ) and ( p_2 ).
( p_1=(0,0) )
( p_2=(2,5) )
( d(p_1,p_2)=square )
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall the distance formula

The distance formula between two points \(P_1=(x_1,y_1)\) and \(P_2=(x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 0,y_1 = 0,x_2=2,y_2 = 5\).

Step2: Substitute the values into the formula

Substitute the values into the formula: \(d=\sqrt{(2 - 0)^2+(5 - 0)^2}\).
First, calculate \((2 - 0)^2=2^2 = 4\) and \((5 - 0)^2=5^2=25\).
Then, \(d=\sqrt{4 + 25}\).

Step3: Simplify the expression

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

Answer:

\(\sqrt{29}\)