Pythagoras' Theorem - X and Y of center of C

Question

I need to find out the $X$ and $Y$ coordinates of the center of $C$.

Say, we have a triangle, $A=5, B=10$. In space, the $A$ goes from $(0,0)$ to $(5,0)$, and $B$ goes from $(0,0)$ to $(0,10)$.

We know $A^2 + B^2 = C^2$, so I know how to get the length of $C$, but how can I calculate the center $X$ and $Y$ position of $C$?

Now I can calculate the length of $C$ by using Pythagoras' theorem - but how can I get the $X$ and $Y$ coordinates of the center of $C$ in an efficient manner?

Answer 1

You have the points $\;A(0,5)\;,\;\;B(10,0)\;$ and you want the middle point of the segment $\;AB\;$, which is simply

$$M=\left(5,\,\frac52\right)$$

In general, the midpoint of the segment of line with end points $\;(x_1,\,y_1)\;,\;\;(x_2,\,y_2)\;$ is the point

$$\left(\frac{x_1+x_2}2\;,\;\frac{y_1+y_2}2\right)$$