Question
From the point $$\left( {4,\,3} \right)$$ a perpendicular is dropped on the $$x$$-axis as well as on the $$y$$-axis. If the lengths of perpendiculars are $$p,\,q$$ respectively, then which one of the following is correct ?
A.
$$p = q$$
B.
$$3p = 4q$$
C.
$$4p = 3q$$
D.
$$p + q = 5$$
Answer :
$$4p = 3q$$
Solution :
$$\eqalign{ & p = \sqrt {{{\left( {4 - 4} \right)}^2} + {{\left( {3 - 0} \right)}^2}} = 3 \cr & q = \sqrt {{{\left( {4 - 0} \right)}^2} + {{\left( {3 - 3} \right)}^2}} = 4 \cr & {\text{Now,}} \cr & 4p = 4 \times 3 = 12 \cr & 3q = 3 \times 4 = 12 \cr & \therefore \,4p = 3q \cr} $$
$$\eqalign{ & p = \sqrt {{{\left( {4 - 4} \right)}^2} + {{\left( {3 - 0} \right)}^2}} = 3 \cr & q = \sqrt {{{\left( {4 - 0} \right)}^2} + {{\left( {3 - 3} \right)}^2}} = 4 \cr & {\text{Now,}} \cr & 4p = 4 \times 3 = 12 \cr & 3q = 3 \times 4 = 12 \cr & \therefore \,4p = 3q \cr} $$