Find the circumcentre of the triangle with ve | vedclass

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Question

(B) Let the vertices of the triangle be $A(0,0)$,$B(3,4)$,and $C(0,4)$.Since the vertices $A(0,0)$ and $C(0,4)$ lie on the $y$-axis,the side $AC$ is v

Vedclass · Accepted Answer

$\left(\frac{3}{2}, 2\right)$

Vedclass · Answer

(B) Let the vertices of the triangle be $A(0,0)$,$B(3,4)$,and $C(0,4)$.Since the vertices $A(0,0)$ and $C(0,4)$ lie on the $y$-axis,the side $AC$ is vertical.The triangle is a right-angled triangle because the side $AC$ (length $4$) is perpendicular to the side $BC$ (which is horizontal,length $3$).In a right-angled triangle,the circumcentre is the midpoint of the hypotenuse.The hypotenuse is the side $AB$ connecting $(0,0)$ and $(3,4)$.The midpoint of $AB$ is given by the formula $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$.Substituting the values: $\left(\frac{0+3}{2}, \frac{0+4}{2}\right) = \left(\frac{3}{2}, 2\right)$.Therefore,the circumcentre is $\left(\frac{3}{2}, 2\right)$.

Find the circumcentre of the triangle with vertices $(0,0), (3,4), \text{and } (0,4)$.

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