Question

The circumcentre of the triangle formed by (2,-5) ,(2,7),(4,7)

Answer 1

Given :  triangle formed by (2,-5), (2, 7), (4,7)

To find : circumcentre of the triangle

Solution:

Let say ( x , y ) is the  circumcenter of triangle formed by

(2,-5), (2, 7), (4,7)

Distance of circumcenter from each vertex is same

(x - 2)² + (y + 5)² = (x - 2)² + (y - 7)² = (x - 4)²  + (y - 7)²

(x - 2)² + (y + 5)² = (x - 2)² + (y - 7)²

=> (y + 5)² =  (y - 7)²

=> y² + 10y + 25 = y² -14y + 49

=> 24y = 24

=> y = 1

(x - 2)² + (y - 7)² = (x - 4)²  + (y - 7)²

=>  (x - 2)²   = (x - 4)²

=> x² -4x + 4 = x² - 8x + 16

=> 4x = 12

=> x = 3

( 3 ,1 ) the  circumcentre of the triangle formed by (2,-5), (2, 7), (4,7)

option 1 is correct

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