Chapter 5.1, Problem 46PPS

To determine

To find: The coordinates of the circum center of the triangle.

Answer to Problem 46PPS

The coordinates of the circumcenter of the triangle is $\left(2\cdot 5,-4\right)$ .

Explanation of Solution

Given information:

The given vertices are $J\left(5,0\right)$ , $K\left(5,-8\right)$ , and $L\left(0,0\right)$ .

Calculation:

The perpendicular bisector of the triangle intersects at a point called the circumcenter that is equidistance from the vertices of the triangle.

The graph for the points $A\left(0,0\right)$ , $B\left(0,6\right)$ , and $C\left(10,0\right)$ is shown in figure (1).

  

Figure (1)

  $\overline{LJ}$ is horizontal, and $LJ=5$ . So, the perpendicular bisector of $\overline{LJ}$ is vertical, and through $\left(2\cdot 5,0\right)$ . The linear equation is $x=2\cdot 5$ .

  $\overline{JK}$ is vertical, and $JK=8$ . So, the perpendicular bisector of $\overline{JK}$ is horizontal, and through $\left(5,-4\right)$ . The linear equation is $y=-4$ .

Circumcenter theorem shows the circumcenter is the intersection point of $x=2\cdot 5$ and $y=-4$ .

Therefore, the coordinates of the circumcenter of the triangle is $\left(2\cdot 5,-4\right)$ .