Question

which equation can be used to determine the distance between the origin and $(-2,-4)$?
$d = \sqrt{(0-(-2))^{2}-(0-(-4))^{2}}$
$d = \sqrt{((0 - 2)+(0 - 4))^{2}}$
$d = \sqrt{(0-(-2))^{2}+(0-(-4))^{2}}$
$d = \sqrt{((0 - 2)-(0 - 4))^{2}}$

Explanation:

Step1: Recall the 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: Identify the points

The origin is \((0,0)\) and the other point is \((-2,-4)\). So \(x_1 = 0,y_1 = 0,x_2=-2,y_2 = -4\).

Step3: Substitute into the formula

Substitute the values into the distance formula: \(d=\sqrt{(0-(-2))^2+(0 - (-4))^2}\).

Answer:

\(d=\sqrt{(0-(-2))^2+(0 - (-4))^2}\) (the third option)