Question
The coordinates of circumcentre of the triangle with vertices (2,3), (4, - 1) and (4,3) are
Answer: Option C
:
C
1st method: - In a right angled triangle
Circumradius = hypotenuse2
The coordinates of circumcentre = (3,1)
2nd method: - If O(x1, y1) is the circumcentre, then OA2=OB2.
(x1−2)2+(Y1−3)2=(X1−4)2+(Y1+1)2
−4X1−6Y1+8X1−2Y1=17−13=4
i.e., 4X1−8Y1=4 or X1−2Y1=1 ..................(I)
OB2=OC2
X1−4)2+(Y1+1)2=(X1−4)2+(Y1−3)2
2Y1+6Y1=8
8Y1=8 ....................(II)
Y1=1
From (i) X1=3
X1,Y1)=(3,1)
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:
C
1st method: - In a right angled triangle
Circumradius = hypotenuse2
The coordinates of circumcentre = (3,1)
2nd method: - If O(x1, y1) is the circumcentre, then OA2=OB2.
(x1−2)2+(Y1−3)2=(X1−4)2+(Y1+1)2
−4X1−6Y1+8X1−2Y1=17−13=4
i.e., 4X1−8Y1=4 or X1−2Y1=1 ..................(I)
OB2=OC2
X1−4)2+(Y1+1)2=(X1−4)2+(Y1−3)2
2Y1+6Y1=8
8Y1=8 ....................(II)
Y1=1
From (i) X1=3
X1,Y1)=(3,1)
Was this answer helpful ?
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