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?

Solution 1:

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.

$$|x_1-x_2|=|y_1-y_2|$$

Solution 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