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  4. The coordinates of the orthocenter of the triangle that has the coordinates of midpoints of its sides as (0,0), (1,2) and (- 6 ,3) is

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Q. 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

NTA AbhyasNTA Abhyas 2020Straight Lines

Solution:

Line joining the midpoints of two sides is $\parallel$ to the third side and half of it.
$\angle O=90^{o}$ (as $AO\bot OB$ )
Hence $P$ will be the orthocentre
Solution
$AOBP$ forms a rectangle.
$\therefore \, \, P=A+B-O$ (using the concept that diagonals bisect each other)
$P(x, y)=\left[\begin{array}{c}x=-6+1-0=-5 \\ y=2+3-0=5\end{array}\right.$