the coordinate of the incenter of the triangle whose vertices are (4,-2 ) (-2,4) and (5,5)
sach , 11 Years ago
Grade 12
Algebra> the coordinate of the incenter of the tri...
1 Answers
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 = (72+12) = 50 = 52
b = |CA| = (4-5)2 + (-2-5)2 = (72+12) = 50 = 52
c = |AB| = (-2-4)2 + (4+2)2 = (36 + 36) = 72 = 62
Coordinates of incentre of traingle ABC are
[(ax1 + bx2 + cx3) / (a+b+c) , (ay1 + by2 + cy3) / (a+b+c)]
i.e. [ {52 .4 + 52 . (-2) + 62 .5 }/ 162 , {52 . (-2) + 52 . 4 + 62 .5 }/ 162 ],
Hence, this gives ( 402/ 162 , 402/ 162)
Hence, the coordinates of the incentre are (5/2, 5/2).
Thanks & Regards
Latika Leekha
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