Question

find the distance ( d(p_1,p_2) ) between the points ( p_1 ) and ( p_2 ).
( p_1=(-3,5);p_2=(2,2) )
( 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 \(d(P_1,P_2)=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1=-3,y_1 = 5,x_2=2,y_2=2\).

Step2: Substitute the values into the formula

Substitute the values into the formula: \((x_2 - x_1)=2-(-3)=2 + 3=5\) and \((y_2 - y_1)=2 - 5=-3\). Then \(d(P_1,P_2)=\sqrt{(5)^2+(-3)^2}\).

Step3: Calculate the squares and sum

Calculate \((5)^2 = 25\) and \((-3)^2=9\). Then \((5)^2+(-3)^2=25 + 9=34\). So \(d(P_1,P_2)=\sqrt{34}\).

Answer:

\(\sqrt{34}\)