Question

The medians AD and BE of a triangle with vertices A(0, b), B(0, 0) and C(a, 0) are perpendicular to each
other if

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The coordinates of the middle points D and E are
$D\equiv (\frac{a}{2},0),E\equiv (\frac{a}{2},\frac{b}{2})$
Slope of median AD is

$m_1=-\frac{2b}{a}$
slope of median BE is
$m_2=-\frac{b}{a}$
since $AD\perp BE$
$\therefore m_1\times m_2=-1\Rightarrow -\frac{2b}{a}\times \frac{b}{a}$
$=-1\Rightarrow a=\pm \sqrt{2}b$