Latika Leekha
Last Activity: 10 Years ago
The given coordinates are (4, -2), (-2,4) and (5,5).
Let us denote them as A(4, -2), B(-2,4) and C(5,5).
Then a = |BC| =

(5+2)
2 + (5-4)
2 =

(7
2+1
2) =

50 = 5

2
b = |CA| =

(4-5)
2 + (-2-5)
2 =

(7
2+1
2) =

50 = 5

2
c = |AB| =

(-2-4)
2 + (4+2)
2 =

(36 + 36) =

72 = 6

2
Coordinates of incentre of traingle ABC are
[(ax1 + bx2 + cx3) / (a+b+c) , (ay1 + by2 + cy3) / (a+b+c)]
i.e. [ {5

2 .4 + 5

2 . (-2) + 6

2 .5 }/ 16

2 , {5

2 . (-2) + 5

2 . 4 + 6

2 .5 }/ 16

2 ],
Hence, this gives ( 40

2/ 16

2 , 40

2/ 16

2)
Hence, the coordinates of the incentre are (5/2, 5/2).
Thanks & Regards
Latika Leekha
askIITians Faculty