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In triangleABC, vertex A is (1, 2). If t...

In `triangleABC`, vertex A is (1, 2). If the internal angle bisector of `angle B` is `2x- y+10=0` and the perpendicular bisector of AC is y = x, then find the equation of BC

Text Solution

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The image D of A in the bisector of `angle B` lies on BC.
Now, the image of A(1,2) in the line 2x-y-10=0 is given by
`(x_(1)-1)/(2) = (y_(1)-2)/(-1) = (-2(2-2+10))/(4+1)`
. `therefore D(x_(1), y_(1)) -=D(-7,6)`

Also, C is the image of A in the perpendicular bisector of AC. The image of A(1,2) in y=x is C(2,1).
Hence the equation of line BC is
. `y-1 = (6-1)/(-7-2)(x-2)`
or 5x+9y-19=0
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