TITLE: How to know if two points are diagonally aligned?
QUESTION [14 upvotes]: If I have two points at different X/Y coordinates, I know that:

They are vertically aligned if both are at the same X coordinate;
They are horizontally aligned if both are at the same Y coordinate.

Based on the X/Y coordinates of one in relation to the other I can also tell the distance between them, etc.
Now, how can you tell that the points are diagonally aligned by following the same logic?

REPLY [18 votes]: If you mean that the line between the two points is at a 45 degree angle to the horizontal (or that the two points would be opposite vertices of a square), then you need to look at the difference between the two X values and the difference between the two Y values.  If those differences are the same, then you have achieved what you are looking for.
$$|x_1-x_2|=|y_1-y_2|$$