Question

The coordinates of the orthocenter of the triangle that has the coordinates of midpoints of its sides as $\left(0,0\right),\left(1,2\right)$ and $\left(-6,3\right)$ is

• A. $\left(0,0\right)$
• B. $\left(-4,5\right)$
• C. $\left(-5,5\right)$
• D. $\left(-4,4\right)$

Answer 1

Answer: (C)

Line joining the midpoints of two sides is $\parallel$ to the third side and half of it.
$\angle O=90^o$ (as $AO\perp OB$ )
Hence $P$ will be the orthocentre

$AOBP$ forms a rectangle.
$\therefore P=A+B-O$ (using the concept that diagonals bisect each other)
$P(x,y)=[\begin{array}{c}x=-6+1-0=-5\\ y=2+3-0=5\end{array}$