Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
What is the question? The two coordinates are $(0,a)$, $(b,0)$ and the line joining these two points can be characterized in many ways such as the convex sum $t(b,0)+(1-t)(0,a) = (tb, (1-t)a)$ for $t\in [0,1]$. – copper.hat Jun 13 '14 at 19:56
If you call the vertices of the triangle which are adjacent to the hypotenuse $p$ and $q$. Then what you are looking for is an equation for the line segment joining $p$ and $q$. @copper.hat I don't think the poster is advanced enough to know what the convex sum is. – James Jun 13 '14 at 19:58
up vote 2 down vote accepted

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).

share|cite|improve this answer
Thank you for your help! – capturographer Jun 13 '14 at 20:07

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.