Question

Determine the coordinates of
the circumcenter of the
triangle whose vertices are
(12,5), (6, -1) and (12,-1).
ps:A.
(2, 37/3)
B.
(-37/3,2)
C.
(-2, 37/3)
D.
(27/3,2)​

Answer 1

Given : A  triangle whose vertices are  (12,5), (6, -1) and (12,-1).

To find : coordinates of  the circumcenter of the  triangle

Solution:

Let say

A = ( 12  , 5)

B = (6 , - 1)

C = ( 12 ,  - 1)

circumcenter is where perpendicular bisector meets

mid point of AB   =   (9 , 2)

Slope of AB = (- 1 - 5) /( 6 - 12)  = 1

Slope of perpendicular to AB  =  - 1

y = - x + c

will pass through 9 , 2

2 = -9  + c  => c = 11

=> y = -x + 11

=> x + y =  11

mid point of AC   =   (12 , 2)

Slope of AB = (- 1 - 5) /( 12 - 12)  = 1/0

Slope of perpendicular to AB  =  0

y =   c

will pass through 12 , 2

y = 2

y = 2  & x = 9

( 9 ,  2)  will be circumcenter  

hence 27/3  , 2  is correct option  

Learn more:

Which of the following is a characteristic of the circumcenter of a ...

https://brainly.in/question/15038473

then circumcentre of triangle is

https://brainly.in/question/2309436