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

Options

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

Answer

B

Explanation

The coordinate of D and E are (a/2, 0) and (a/2,b/2) respectively.
Now, `m_(1)`=Slope of AD `=(b-0)/(0-a//2)=-(2b)/(a)`
`m_(2)` =Slope of BE `=(b//2-0)/(a//2-0)=(b)/(a)`
Since AD and BE are perpendicular . Therefore,
`m_(1)m_(2)=-1-(2b)/(a)xx(b)/(a)=-1 implies a=pmsqrt(2)b`