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Question

The equation of the three sides of a triangle are x=2,y+1=0 and x+2y=4. The coordinates of the circumcentre of the triangle are

A
(4,0)
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B
(2,1)
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C
(0,4)
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D
(1,2)
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Solution

The correct option is A (4,0)
Sides of the given triangle:

x=2,y+1=0,x+2y=4

Line x=2 will cut x-axis at (2,0).

Line y+1=0 will cut y-axis at (0,1).

Line x+2y=4 will intersect with line x=2 in point (2,1) i.e., C(2,1)

Line x+2y=4 will intersect line y+1=0 in point (6,1) i.e., A(6,1)

Now,

For ABC, midpoint of AC is the circumcentre.
circumcentre =[(2+6)2,(11)2]

(4,0)\
Hence the circumcentre of the triangle is (4,0).

1260054_1079810_ans_509e73018f72435b9519f216f67938eb.png

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