(B) Let the angle bisector of $B$ be $L: y = x$. The reflection of vertex $A(3, 5)$ across the line $y = x$ will lie on the line $BC$. To find the ref

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(B) Let the angle bisector of $B$ be $L: y = x$. The reflection of vertex $A(3, 5)$ across the line $y = x$ will lie on the line $BC$. To find the reflection $(x', y')$ of point $(x_0, y_0)$ across the line $y = x$,we swap the coordinates: $(x', y') = (y_0, x_0)$. Thus,the reflection of $A(3, 5)$ is $(5, 3)$. Therefore,the point $(5, 3)$ must lie on the line $BC$.

Class 11 Mathematics Straight Line Foot of perpendicular, Image of a point and Reflexive properties

Difficult

In a triangle $ABC$,$A(3, 5)$ is a vertex. If the internal angle bisector of $B$ is $y = x$,then which of the following points must lie on the line $BC$?

A
$(0, 10)$
B
$(5, 3)$
C
$(-3, -7)$
D
$(5, 4)$

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Straight Line

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Foot of perpendicular, Image of a point and Reflexive properties

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In a triangle $ABC$,$A(3, 5)$ is a vertex. If the internal angle bisector of $B$ is $y = x$,then which of the following points must lie on the line $BC$?

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