The circumcentre of the triangle with vertice | vedclass

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Question

(C) Let the vertices of the triangle be $A(6,0)$,$B(0,0)$,and $C(0,8)$.Since the vertices $A(6,0)$ and $C(0,8)$ lie on the $x$-axis and $y$-axis respe

Vedclass · Accepted Answer

$(3,4)$

Vedclass · Answer

(C) Let the vertices of the triangle be $A(6,0)$,$B(0,0)$,and $C(0,8)$.Since the vertices $A(6,0)$ and $C(0,8)$ lie on the $x$-axis and $y$-axis respectively,and the vertex $B$ is at the origin $(0,0)$,the triangle is a right-angled triangle with the right angle at $B(0,0)$.For a right-angled triangle,the circumcentre is the midpoint of the hypotenuse.The hypotenuse is the line segment joining $A(6,0)$ and $C(0,8)$.The midpoint of the hypotenuse is given by the formula $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$.Substituting the coordinates of $A$ and $C$: $\left( \frac{6 + 0}{2}, \frac{0 + 8}{2} \right) = \left( \frac{6}{2}, \frac{8}{2} \right) = (3,4)$.Thus,the circumcentre is $(3,4)$.

The circumcentre of the triangle with vertices $(6,0), (0,0)$ and $(0,8)$ is $\ldots \ldots \ldots$

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