Straight LineHardBloom L3
Question
Two vertices of a triangle are $(5, - 1)$ and $( - 2,3)$. If orthocenter of the triangle is origin, then the co-ordinates of third vertex is :
Options
A.$(4,7)$
B.$(3,7)$
C.$( - 4, - 7)$
D.$(4, - 7)$
Solution
Sol. [Key Concept: Orthocenter at $O$ ⇒ third vertex from $OC \perp AB$ and $OA \perp BC$.]
Slope of $AH = \frac{k}{h} = \frac{7}{4}$
$$\text{~}\text{Slope of}\text{~}AC = \frac{k + 1}{h - 5} = \frac{2}{3}$$
So, $3\left( \frac{7}{4}h + 1 \right) = 2(h - 5)$
$$\Rightarrow \ \begin{matrix} & h = - 4,k = - 7 \\ & A = ( - 4, - 7) \end{matrix}$$
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