Question

Find the coordinates of the circumcenter triangle abc with vertices A (0,0) B(3,0) C(3,2)

Answer 1

Answer:

The coordinates of the circumcenter of triangle ABC is $(1.5,1)$.

Step-by-step explanation:

The circumcenter of triangle ABC is the point of intersection of any two perpendicular bisectors of any two sides of the given triangle.

The equation of the perpendicular bisector of side B(3,0) and C(3,2) is $y=1$.

Since the midpoint of AB is $(3,1)$ and its slope is undefined. The perpendicular bisector has a slope of zero. The equation of such line is $y=y_1$.

Also the equation of the perpendicular bisector of A(0,0) and B(3,0) is $x=1.5$. The reason is that the midpoint of AB is $(1.5,0)$ and its slope is zero. The perpendicular bisector will have an undefined slope. The equation of such line is given by $x=x_1$.

These two perpendicular bisectors will intersect at $(1.5,1)$. These are the coordinates of the circumcenter of the triangle.