question_answer

Orthorcentre of triangle with vertices (0, 0), (3, 4) and (4, 0) is    [IIT Screening 2003]

A) \[\left( 3,\,\frac{5}{4} \right)\]

B) (3, 12)

C) \[\left( 3,\,\frac{3}{4} \right)\]

D) (3, 9)

Correct Answer: C

Solution :

\[BD\bot AC\]. Slope of \[BD=-\frac{3}{4}\] Equation of \[BD\], \[3x+4y-12=0;AE\,\bot \,BC\] .....(i) Slope of \[AE=\frac{1}{4}\] Equation of AE, \[x-4y=0\] .....(ii) From equation (i) and (ii), \[x=3,y=\frac{3}{4}\] \ orthocentre of the triangle is \[\left( 3,\frac{3}{4} \right)\]