Question

The coordinates of the circumcentre of the triangle with vertices $(2, 3), (4, -1)$ and $(4, 3)$ are

• A. (2, 3)
• B. (1, 3)
• C. (3, 1)
• D. (3, 2)

Answer 1

Answer: (C)

(3, 1)

Answer 2

Coordinates of A, B, Care (2, 3) (4, -1), (4, 3). respectively.
Slope $m_1$ of BC is $\frac{3 -(-1)}{4-4} =\infty$
Slope $m_2$ of AC is $\frac{3 -3}{4-2} = 0$

$\therefore \:\:\:\Delta ABC$ is right angled at C (4, 3)
$\therefore$ Circumcentre of $\Delta ABC$ is the mid-point of the hypotenuse AB which is
$\left( \frac{4 + 2}{2} , \frac{3 -1}{2} \right)$ i.e.., $(3,1)$