Question

What are the coordinates of the circumcenter of this triangle?

Answer 1

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

$A(-2,5),B(-2,-1),C(8,-1)$

step 1

Find the midpoint AB

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M=(\frac{-2-2}{2},\frac{5-1}{2})$

$M_A_B=(-2,2)$

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)

$y=2$ -----> equation A

step 3

Find the midpoint BC

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M=(\frac{-2+8}{2},\frac{-1-1}{2})$

$M_B_C=(3,-1)$

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)

$x=3$ -----> equation B

step 5

Find the circumcenter

The circumcenter is the intersection point between the equation A and equation B

$y=2$ -----> equation A

$x=3$ -----> equation B

The intersection point is (3,2)

therefore

The coordinates of the circumcenter of this triangle are (3,2)