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The medians A D\ a n d\ B E of a triangl...

The medians `A D\ a n d\ B E` of a triangle with vertices `A(0, b),\ B(0,0)\ a n d\ C(a ,0)` are perpendicular to each other, if `a=b/2` b. `b=a/2` c. `a b=1` d. `a=+-sqrt(2)b`

Text Solution

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A median in a triangle is a line passing thought a vertex and through the midpoint of the side opposite to the vertex.
`{D} `is the midpoint of side `{BC}`
`{D}=(\frac{{a}}{2}, 0)`
slope of `AD=\frac{{b}-0}{0-{a} / 2}=\frac{-2 {~b}}{{a}}`
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Knowledge Check

  • The medians AD and BE of the triangle with vertices A(0, b), B(0, 0) and C(a, 0) are mutually perpendicular if

    A
    `b = a sqrt(2)`
    B
    `a = b sqrt(2)`
    C
    `b = - a sqrt(2)`
    D
    `a = -b sqrt(2)`

  • The medians AD and BE of the triangle with vertices A(0,b),B(0,0) and C(a,0) are mutually perpendicular if

    A
    `b=sqrt(2)a`
    B
    `a=sqrt(2)b`
    C
    `b=-sqrt(2)a`
    D
    `a=-sqrt(2)b`

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