Question

distance formula
$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
$(x_1,y_1)=(\square,\square)\\ (x_2,y_2)=(\square,\square)$
$d = \sqrt{(\square - \square)^2+(\square - \square)^2}$
$d = \sqrt{(\square)^2+(\square)^2}$
$d = \sqrt{\square+\square}$
$d = \sqrt{\square}$
$d =$

Explanation:

Step1: Assume two points

Let $(x_1,y_1)=(a,b)$ and $(x_2,y_2)=(c,d)$

Step2: Substitute into formula

$d = \sqrt{(c - a)^2+(d - b)^2}$

Step3: Expand squares

$d=\sqrt{(c^2 - 2ac+a^2)+(d^2 - 2bd + b^2)}$

Step4: Combine like - terms

$d=\sqrt{c^2+a^2 + d^2 + b^2-2ac - 2bd}$

Answer:

$d=\sqrt{c^2+a^2 + d^2 + b^2-2ac - 2bd}$