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Question

The incentre of the triangle formed by the vertices A(−36,7), B(20,7) and C(0,−8) is

A
(0,1)
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B
(1,0)
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C
(12,1)
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D
(1,12)
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Solution

The correct option is B (1,0)
Assuming the vertices be
A(x1,y1)=(36,7)
B(x2,y2)=(20,7)
C(x3,y3)=(0,8)
Now, the side lengths are
a=BC=25 units
b=AC=39 units
c=AB=56 units
Now, the incentre,
I=(ax1+bx2+cx3a+b+c,ay1+by2+cy3a+b+c)
I=(25(36)+39(20)+56(0)25+39+56,25(7)+39(7)+56(8)25+39+56)I=(25(36)+39(20)120,64(7)56(8)120)I=(20(45+39)120,64(77)120)
I=(1,0)

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