Right-angled triangles on a graph My question today is whether or not a concise formula has been discovered for the coordinates along the hypotenuse of a right-angled triangle when plotted on a graph. I have been working on this and have discovered a formula which seems to work, but of course, it is not definite and I will need your help. If you test it on a few right-angled triangles, I would be very grateful. However, it does depend on where you plot the triangle and which side the right angle is. If the right angle sits at ($0, 0$), the formula is $a(b-x)/b$ where $a$ is the side that sits on the y-axis, $b$ is the side that sits on the x-axis and $x$ is the x-coordinate to which you want to find the y-coordinate of along the hypotenuse. This formula is changed only slightly when the right angle is situated on the other side. I believe this formula to be $ax/b$. Sorry for such a long-winded question. Thank you.

The formula is well known and can be written in many ways.

The hypotenuse is a segment of a line through the corners.

The corners you describe are $(0,a),(b,0)$. A formula for a line through these points is $x \mapsto (1- { x \over b}) a $ (which is the same as the formula you have written above).