Question

given two points ((x_1, y_1)), ((x_2, y_2)) the distance between them is: (sqrt{(x_2 + y_1)^2 - (x_2 + x_1)^2}) (yellow card), (sqrt{(y_1 - y_2)^2 + (x_2 - x_1)^2}) (blue card), (sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}) (orange card), (sqrt{(y_2 - y_1) + (x_2 - x_1)}) (cyan card)

Explanation:

Step1: Recall distance formula logic

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ comes from the Pythagorean theorem, using squared differences of coordinates.

Step2: Match to correct formula

The valid formula uses squared differences of $x$-coordinates and $y$-coordinates, summed under a square root. Since $(y_1-y_2)^2=(y_2-y_1)^2$ and $(x_2-x_1)^2=(x_1-x_2)^2$, the correct expression is $\sqrt{(y_1 - y_2)^2 + (x_2 - x_1)^2}$ (equivalent to $\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$).

Answer:

B. $\sqrt{(y_1 - y_2)^2 + (x_2 - x_1)^2}$ (and the orange option $\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$ is also mathematically equivalent, but the blue option is explicitly a correct standard form)