A) \[\left( \frac{5}{2},\,\,\frac{3}{4} \right)\]
B) \[\left( \frac{-5}{2},\,\,\frac{3}{4} \right)\]
C) \[\left( -5,\,\,\frac{3}{2} \right)\]
D) \[(0,\,\,0)\]
Correct Answer: D
Solution :
\[\Delta AOB\]is the given triangle. Slope of\[AB=\frac{\frac{3}{2}-9}{0+5}=\frac{3}{10}\] Slope of\[BO=\frac{0-0}{0+5}=0\] The equation of line passing through\[A\]and perpendicular to\[BO\] is\[y-0=0\left( x-\frac{3}{2} \right)\] \[\Rightarrow \] \[y=0\] ... (i) and equation of line passing through 0 and perpendicular to\[AB\]is\[y-0=\frac{10}{3}(x-0)\] \[\Rightarrow \] \[y=-\frac{10}{3}x\] ? (ii) The intersection point of Eqs. (i) and (ii) is (0, 0), which is the required orthocentre.You need to login to perform this action.
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