Two verities of a triangle are $(5,\ - 1)$ and $( - 2,\ 3)$. If the orthocenter of the triangle is the origin, then coordinates of third vertex are

Question

Dr. Abubacker · Accepted Answer

(b)
Let the coordinates of the third vertex $A$ be $(h,\ k)$
[image:10_image12.emf]
Also, $AD\bot BC$
$	herefore\frac{k - 0}{h - 0} 	imes \left( \frac{4}{- 7} ight) = - 1$
$\Rightarrow \ \ 7h = 4k$ …(i)
and $OB\bot AC$
$\Rightarrow \frac{k - 3}{h + 2} 	imes \left( - \frac{1}{5} ight) = - 1$
$\Rightarrow 5h - k + 13 = 0$ …(ii)
On solving Eqs. (i) and (ii), we get
Hence, the coordinates of third vertex are $( - 4,\  - 7)$

Q. Two verities of a triangle are $(5,\ - 1)$ and $( - 2,\ 3)$. If the orthocenter of the triangle is the origin, then coordinates of third vertex are

Explanation

Reviewed by Dr. Abubacker

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