Question

In given figure let $A(0,0)$ and $B(8,0)$ be two vertices of a right angled triangle whose hypotenuse is $BC$. If the circumcentre is $(4,2)$, then the point $C$ is

• A. $(2,4)$
• B. $(0,8)$
• C. $(0,4)$
• D. $(0,6)$
• E. $(2,8)$

Answer 1

Answer: (C)

$(0,4)$

In a right angle triangle, the mid-point of the hypotenuse is the circumcentre.
Let the coordinates of the point $C$ be $(x,y)$.

Then,by using Midpoint formula $X=\left(\frac{x_1+x_2}{2}\right)andY=\left(\frac{y_1+y_2}{2}\right)$

$\therefore (\frac{8+x}{2},\frac{0+y}{2})=(4,2)$

$\Rightarrow \frac{8+x}{2}=4$ and $\frac{0+y}{2}=2$

$\Rightarrow x=0$ and $y=4$

Hence, coordinates of $C$ are $(0,4)$.