Chapter 6, Problem 13STP

To determine

To calculate:

Coordinates of the circumcenter of the given triangle.

Answer to Problem 13STP

Coordinates of the circumcenter of the given triangle is $△\mathrm{X}\mathrm{Y}\mathrm{Z}$

  $\left(\mathrm{b},\mathrm{a}\right)$ .

Explanation of Solution

Given information:

  

Assume, $\mathrm{A}\mathrm{B}\mathrm{C}$ are the vertices then,

  $\mathrm{A}\left(0,4\right),\mathrm{B}\left(0,0\right),\mathrm{C}\left(2,0\right)$

So mid point of the

  $\begin{array}{l}\mathrm{A}\mathrm{B}=\left(\frac{0+0}{2},\frac{4+0}{2}\right)\\ \mathrm{A}\mathrm{B}=\left(0,2\right)\end{array}$

Slope of $\mathrm{A}\mathrm{B}$ ,

  $=\frac{0-0}{0-2}=0$

Need at least two perpendicular bisectors for finding out circumcenter which is their intersection.

Using both legs, equations $\mathrm{x}=\mathrm{b}$ and $\mathrm{y}=\mathrm{a}$ as the equations of perpendicular bisectors of $\overline{\mathrm{X}\mathrm{Z}}$ and $\overline{\mathrm{X}\mathrm{Y}}$ .

  

Therefore, circumcenter of $△\mathrm{X}\mathrm{Y}\mathrm{Z}$ is $\left(\mathrm{b},\mathrm{a}\right)$ .