Question

Explain why the order of the coordinates does not matter when calculating length in geometry?

Answer 1

$A=(x_1,y_1)\ \ \ and\ \ \ B=(x_2,y_2)\\\\|AB|= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} =\\\\= \sqrt{[-(x_2-x_2)]^2+[-(y_2-y_1)]^2}=\\\\ =\sqrt{(x_2-x_2)^2+(y_2-y_1)^2}=|BA|$

Answer 2

$P(x_1;\ y_1);\ Q(x_2;\ y_2)\\\\|PQ|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|QP|=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}=\sqrt{[-1(x_2-x_1)]^2+[-1(y_2-y_1)]^2}\\\\=\sqrt{(-1)^2(x_2-x_1)^2+(-1)^2(y_2-y_1)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|PQ|=|QP|$