# How to find a point on a triangle?

And a happy new year to you all!

How would you calculate the coordinates of a point on the edge of a triangle?

My question is very similar to this one but I need to work out a number of points along the edge of the triangle - not the projection of the height, as per the link previously.

Apologies, my maths skills are not strong at all.

Thanks in advance.

Cheers, Rudy

• If you have coordinates of the corners of the triangle? If so, $\lambda A + (1-\lambda)B$ for $\lambda \in [0,1]$ will give you all points between the point $A$ and $B$. – YukiJ Jan 5 '17 at 23:26
• Thank you Yuki. TBH I have no idea what that means, but I will work that out. – Rudy N Jan 5 '17 at 23:33
• If I may ask, how would this example look please, if you could show me the steps to the solution? A = (0,0), and B = (2,4) – Rudy N Jan 6 '17 at 2:21
• See the answer by Siong below. – YukiJ Jan 6 '17 at 7:01

## 1 Answer

The points along the edge $AB$ can be characterized by $$\lambda A + (1-\lambda)B$$ where $\lambda \in [0,1]$.

Credit: YukiJ answered this in the comment.

For example, If $A=(0,0)$ and $B=(2,4)$

The points can be characterized by

$$\lambda(0,0)+(1-\lambda) (2,4)=(2(1-\lambda),4(1-\lambda))$$

If we substitute $\lambda=0$, we obtain $(2,4)=B$.

If we substitute $\lambda =1$, we obtain $(0,0)=A$.

If we substitute $\lambda = \frac12$, we obtain $(1,2)$ which is the mid point.

As $\lambda$ increases, we move from point $B$ to point $A$.