Question
Question: If equation of three sides of a triangle are \(x = 2,\) \(y + 1 = 0\) and \(x + 2y = 4\) then co-ord...
If equation of three sides of a triangle are x=2, y+1=0 and x+2y=4 then co-ordinates of
circumcentre of this triangle are.
A
(4, 0)
B
(2, –1)
C
(0, 4)
D
(–1, 2)
Answer
(4, 0)
Explanation
Solution
Equations of three sides of a triangle are
x=2,y+1=0and x+2y=4
Co-ordinates of point of intersection of the x=2 and y+1=0 is (2, –1)
Co-ordinates of point of intersection of x=2 and x+2y=4 is (2, 1)
Co-ordinates of point of intersection of y+1=0 and x+2y=4 is (6, –1)
Let Co-ordinates of circumcentre is (x, y)
(x−2)2+(y+1)2=(x−2)2+(y−1)2
(y+1)2=(y−1)2; y2+2y+1=y2−2y+1
4y=0, y=0 and (x−2)2+(y−1)2=(x−6)2+(y+1)2
In this equation put y=0
(x−2)2+(0−1)2=(x−6)2+(0+1)2
(x−2)2+1=(x−6)2+1; (x−2)2−(x−6)2=0
(x−2+x−6)(x−2−x+6)=0
4(2x−8)=0⇒ 8(x−4)=0; x−4=0 ⇒ x=4
∴ Co-ordinates of circumcentre is (4, 0).