If A(x_1, y_1),B(x_2, y_2),and C(x_3, y_3) ar | vedclass

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Question

(A) The coordinates of the excentre opposite to vertex $A$ are given by $\left( \frac{-ax_1 + bx_2 + cx_3}{-a + b + c}, \frac{-ay_1 + by_2 + cy_3}{-a

Vedclass · Accepted Answer

$\left( \frac{ax_1 - bx_2 + cx_3}{a - b + c}, \frac{ay_1 - by_2 + cy_3}{a - b + c} \right)$

Vedclass · Answer

(A) The coordinates of the excentre opposite to vertex $A$ are given by $\left( \frac{-ax_1 + bx_2 + cx_3}{-a + b + c}, \frac{-ay_1 + by_2 + cy_3}{-a + b + c} \right)$.Similarly,the coordinates of the excentre opposite to vertex $B$ are given by $\left( \frac{ax_1 - bx_2 + cx_3}{a - b + c}, \frac{ay_1 - by_2 + cy_3}{a - b + c} \right)$.Comparing this with the given options,option $A$ is correct.

If $A(x_1, y_1)$,$B(x_2, y_2)$,and $C(x_3, y_3)$ are the vertices of a triangle with side lengths $a, b, c$ opposite to vertices $A, B, C$ respectively,then the excentre with respect to vertex $B$ is:

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