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The orthocenter of the triangle formed b...

The orthocenter of the triangle formed by the lines `xy=0 and x+y=1` is

A

`(1//2,1//2)`

B

`(1//3,1//3)`

C

`(0,0)`

D

`(1//4,1//4)`

Text Solution

Verified by Experts

The correct Answer is:
3
The lines by which triangle is formed are `x=0,y=0and x+y=1`. Clearly , it is a right triangle . We know that in a right angled triangle , the orthocenter coincides with the vertex at which right angles is formed . Therefore , the orthocenter is (0,0).
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Knowledge Check

  • Orthocentre of the triangle formed by the lines x+y=1, x=0 and y=0 is-

    A
    `(0,1)`
    B
    `(0,0)`
    C
    `(1,0)`
    D
    `(1,1)`

  • The triangle formed by the lines x+y =0,3x+y=4 and x+3y=4 is-

    A
    isosceles
    B
    equilateral
    C
    right angled
    D
    isosceles right angled

  • The orthocentre of the triangle formed by the lines x+y=1,2x+3y=6 and 4x-y+4=0 lies in

    A
    I quadrant
    B
    II quadrant
    C
    III quadrant
    D
    IV quadrant

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