Question

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

Answer 1

`P(x_1;\ y_1);\ Q(x_2;\ y_2)\\\\|PQ|=√((x_2-x_1)^2+(y_2-y_1)^2)\\\\|QP|=√((x_1-x_2)^2+(y_1-y_2)^2)=√([-1(x_2-x_1)]^2+[-1(y_2-y_1)]^2)\\\\=√((-1)^2(x_2-x_1)^2+(-1)^2(y_2-y_1)^2)=√((x_2-x_1)^2+(y_2-y_1)^2)\\\\|PQ|=|QP|`

Answer 2

`A=(x_1,y_1)\ \ \ and\ \ \ B=(x_2,y_2)\\\\|AB|= √((x_1-x_2)^2+(y_1-y_2)^2) =\\\\= √([-(x_2-x_2)]^2+[-(y_2-y_1)]^2)=\\\\ =√((x_2-x_2)^2+(y_2-y_1)^2)=|BA|`