Question

Find the circumcentre of the triangle whose vertices are (-2, -3), (- 1, 0), (7, - 6).

Answer 1

Find the circumcentre of the triangle whose vertices are (-2, -

Answer 2

Circumcentre is (7,-2)

Step-by-step explanation:

Let A(-2, -3), B(-1, 0) and C(7, -6) be the vertices of the given triangle. Let P(x, y) be the circumcentre and PA, PB and PC be its circum-radii.

PA = PB = PC

PA² = PB² = PC²

(x+2)² + (y+3)² = (x+1)² + (y-0)²

x² + 4 + 2x + y² + 9 +6y = x² + 1 + 2x + y²

6y = -12

Therefore y = -2

Also, (x+1)² + (y-0)² = (x-7)² + (y+6)²

 x² + 2x + 1 + y² = x² + 49 -14x + y² + 12y + 36

 12x = 84

Therefore x = 7

So the coordinates of the circumcentre are P(7,-2)