The foot of the perpendicular drawn from the origin, on the line, 3 x+y= ( 0) is P . If the line meets x -axis at A and y -axis at B , then the ratio B P: P A is

Step-by-step solution

Equation of the line, which is perpendicular to the line, 3 x+y= ( 0) and passing through origin, is given by x-0 3 = y-0 1 =r For foot of perpendicular r= -((3 0)+(1 0)- ) 3^2+1^2 = 10 So, foot of perpendicular P= ( 3 10 , 10 ) Given the line meets X -axis at A= ( 3 , 0 ) and meets Y -axis at B=(0, ) So, aligned &B P= ( 3 10 )^2+ ( 10 - )^2 B P= 9 ^2 100 + 81 ^2 100 & B P= 90 ^2 100 & Now, P A= ( 3 - 3 10 )^2+ (0- 10 )^2 & P A ^2 900 + ^2 100 P A= 10 ^2 900 aligned Therefore B P: P A=3: 1