Question

Explain why point ​A​(1, -2) is different from point ​B​(-2, 1).

Answer 1

Points are given as (x, y) - an x-coordinate and a y-coordinate. If you swap the x and y values, it's not necessarily going to be in the same location.

But really, this is like asking why 2 is different from -1.

Answer 2

You represent those points on a graph consisting of two axis - x and y.
Lets simplify the problem a little: we will represent A(1) and B(-2) (only the x values) on one graph that will have only x axis.

Now, lets try to represent only the y values of the equation on the same kind of graph (A(-2), B(1)):
As you an see, in neither first or second graph did the points overlap (that would mean that the points are equal), now to really make sure we didn't make a mistake lets represent the graph with original - x and y axis combined:

As you can see, they really aren't the same points! ;)

Answer 3

And sorry for my clumsy drawings!

Answer 4

(Actually, you could have proved that they aren't the same points by just graphing the last graph, however, I wanted to make sure that you understood how it worked)

Answer 5

A and B are points in the four and second quadrant respectively.