Question

find the distance ( d(p_1, p_2) ) between the points ( p_1 ) and ( p_2 ).( p_1 = (2, -3); p_2 = (4, 6) )( d(p_1, p_2) = square )(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: Assign coordinates

Let $(x_1,y_1)=(2,-3)$ and $(x_2,y_2)=(4,6)$

Step3: Compute coordinate differences

$x_2-x_1=4-2=2$, $y_2-y_1=6-(-3)=9$

Step4: Square and sum differences

$(2)^2+(9)^2=4+81=85$

Step5: Take square root

$d=\sqrt{85}$

Answer:

$\sqrt{85}$