Answer:
The answer is the option B
The circumcenter of triangle ABC is the point
Step-by-step explanation:
we know that
The circumcenter of a triangle, is the point where the perpendicular bisectors of a triangle meets
In this problem we have the coordinates of the triangle ABC
Step 1
Find the slope of the side AB
The side AB is a vertical side (parallel to the y-axis)
The slope of the side AB is undefined
we know that
The perpendicular line to the side AB will be a horizontal line (parallel to the x-axis)
The equation of the perpendicular bisector to the side AB will be the y-coordinate of the midpoint AB
Step 2
Find the y-coordinate of midpoint AB
we know that
The formula to calculate the y-coordinate of the midpoint between two points is equal to
we have
Substitute the values
therefore
The equation of the perpendicular bisector to the side AB is
------> equation A
Step 3
Find the slope of the side BC
The side BC is a horizontal side (parallel to the x-axis)
The slope of the side BC is zero
we know that
The perpendicular line to the side BC will be a vertical line (parallel to the y-axis)
The equation of the perpendicular bisector to the side BC will be the x-coordinate of the midpoint BC
Step 4
Find the x-coordinate of midpoint BC
we know that
The formula to calculate the x-coordinate of the midpoint between two points is equal to
we have
Substitute the values
therefore
The equation of the perpendicular bisector to the side BC is
------> equation B
Step 5
Find the circumcenter of triangle ABC
To calculate the circumcenter
Solve the system of equations compound by equation A and equation B
------> equation A
------> equation B
The intersection point is -------> the circumcenter of triangle ABC
see the attached figure to better understand the problem