Answer:
The coordinates of the circumcenter of this triangle are (3,2)
Step-by-step explanation:
we know that
The circumcenter is the point where the perpendicular bisectors of a triangle intersect
we have the coordinates
[tex]A(-2,5),B(-2,-1),C(8,-1)[/tex]
step 1
Find the midpoint AB
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M=(\frac{-2-2}{2},\frac{5-1}{2})[/tex]
[tex]M_A_B=(-2,2)[/tex]
step 2
Find the equation of the line perpendicular to the segment AB that passes through the point (-2,2)
Is a horizontal line (parallel to the x-axis)
[tex]y=2[/tex] -----> equation A
step 3
Find the midpoint BC
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
substitute the values
[tex]M=(\frac{-2+8}{2},\frac{-1-1}{2})[/tex]
[tex]M_B_C=(3,-1)[/tex]
step 4
Find the equation of the line perpendicular to the segment BC that passes through the point (3,-1)
Is a vertical line (parallel to the y-axis)
[tex]x=3[/tex] -----> equation B
step 5
Find the circumcenter
The circumcenter is the intersection point between the equation A and equation B
[tex]y=2[/tex] -----> equation A
[tex]x=3[/tex] -----> equation B
The intersection point is (3,2)
therefore
The coordinates of the circumcenter of this triangle are (3,2)
