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Let in Δ A B C coordinates of vertex A is ( 0 ,   0 ) . Equation of the internal angle bisector of ∠ A B C is x + y - 1 = 0 and mid-point of B C is ( 1 ,   3 ) . The ordinate of vertex C is

Correct answer

6

Step-by-step solution

Reflection of A   ( 0 ,   0 ) about the line x + y - 1 = 0 is ( 1 ,   1 ) which lies on side B C Equation of B C is x = 1 since, line is passing through ( 1 , 1 ) and ( 1 ,   3 ) ⇒ B is the point of intersection of x = 1 and x + y - 1 = 0 ⇒ coordinates of B is ( 1 ,   0 ) ⇒ coordinates of C is ( 1 ,   6 ) ∵ mid point of B and C is ( 1 ,   3 )

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