question_answer

The foot of the perpendicular from\[(-2,3)\]to the line\[2x-y=0\]:

A)  \[(-2,3)\]                            

B)  (2, 1)    

C)         (3, 2)                    

D)         (1, 2)

E)  \[(-3,-2)\]

Correct Answer: B

Solution :

Let AB be the line \[2x-y-3=0\]      ...(i) Its slope = 2. Slope of \[PM=-\frac{1}{2}\] Equation of PM is \[y-3=-\frac{1}{2}(x+2)\] \[\Rightarrow \] \[x+2y-4=0\]                                    ...(ii) On solving Eqs. (i) and (ii), we get \[x=2,\text{ }y=1\] \[\therefore \]Foot of perpendicular is (2, 1).