Question

find the distance ( d(p_1, p_2) ) between the points ( p_1 ) and ( p_2 ).( p_1 = (-5, 4) )( p_2 = (1, 2) )( 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 values to variables

Let $(x_1,y_1)=(-5,4)$ and $(x_2,y_2)=(1,2)$. Substitute into the formula:
$d=\sqrt{(1-(-5))^2+(2-4)^2}$

Step3: Simplify inside the square root

Calculate the differences first:
$d=\sqrt{(6)^2+(-2)^2}=\sqrt{36+4}$

Step4: Sum and simplify the radical

Add the terms inside the root:
$d=\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}$

Answer:

$2\sqrt{10}$