AP EAMCET2001MathematicsStraight Lines
The incentre of triangle formed by the lines x+y=1, x=1, y=1 is
Options
- A(1- 1 2 , 1- 1 2 )
- B(1- 1 2 , 1 2 )
- C( 1 2 , 1 2 )
- D( 1 2 , 1- 1 2 )
Correct answer
C. ( 1 2 , 1 2 )
Step-by-step solution
From the figure, A (x₁, y₁ )=(1,0) (0, 1 ) aligned B (x₂, y₂ ) & =(1,1) and C (x₃, y₃ ) & =(0,1) a=B C & = (1-0)^2+(1-1)^2 =1 b=C A & = (1-0)^2+(0-1)^2 = 1+1 = 2 c=A B & = (1-1)^2+(1-0)^2 =1 aligned Incentre of triangle aligned & = ( a x₁+b x₂+c x₃ a+b+c , a y₁+b y₂+c y₃ a+b+c ) & = ( 1+ 2 1+1+ 2 , 2 +1 1+1+ 2 )= ( 1+ 2 2+ 2 , 1+ 2 2+ 2 ) & = ( 1+ 2 2 (1+ 2 ) , 1+ 2 2 (1+ 2 ) )= ( 1 2 , 1 2 ) aligned