# How to know if two points are diagonally aligned?

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?

• Do you mean that the line between them is at a 45 degree angle to horizontal? – turkeyhundt Mar 17 '15 at 22:01
• Yes, exactly... – Fernando Aires Castello Mar 17 '15 at 22:05

$$|x_1-x_2|=|y_1-y_2|$$
If they are diagonally aligned in one direction, the difference in coordinates will be the same. So $(1,5)$ and $(9,13)$ are on a diagonal because $5-1=13-9$ Can you do the other diagonal? Hint: two point form for a line