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Question

If A(1,3) and C(25,25) are the vertices of a ABC and the equation of the internal angle bisector of ABC is x+y=2, then

A
the equation of line BC is 7x3y+4=0
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B
the equation of line BC is 7x+3y+4=0
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C
B(52,92)
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D
B(52,92)
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Solution

The correct option is D B(52,92)

Let the image of A(1,3) w.r.t. x+y=2 be D(a,b), so
a11=b31=2(1+32)2D=(1,1)

So equation of line BC is
y1=25125+1(x+1)7x+3y+4=0

Therefore, vertex B is point of the intersection of 7x+3y+4=0 and x+y=2
i.e. B(52,92)

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