Question

What are the coordinates of the circumcenter of a triangle with vertices F(0,1) G(3,1) and H(3,5)?

Answer 1

Explanation:

Consider a triangle whose vertices are F(0,1), G(3,1) and H(3,5), Now, formula for distance between two points is given by:

D=
`\sqrt{(x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)}`

Therefore, FG=
`\sqrt{(3-0)^(2)+0^(2)`=3

GH=
`\sqrt{(3-3)^(2)+(5-1)^(2)}`=4

and FH=
`\sqrt{(3)^(2)+(4)^(2) }`=
`√(9+16)=5`

Since,
`FH^(2)=FG^(2)+GH^(2)`, therefore angle G becomes 90°.

thus, circumcentre lies on the middle of the FH.

Therefore, Circumcentre=
`((3+0)/(2),(5+1)/(2))`

=
`((3)/(2),3)`