Question

If 1,p/3 is the mid point of the line segment joining the points (2,0) and (0,2/9),then show that the line 5x+3y+2=0 passes through the point (-1,3p)

Answer 1

If 1,p/3 is the mid point of the line segment joining the points (2,0) and (0,2/9),
then 
(2+0)/2 = 1 and (0 +2/9)/2 = p/3
2 / 9*2 = p/3
1/9 = p/3 
1/3 = p


the point that passes the line 5x+3y+2=0  is (-1,3p)
put p in (-1,3p)
so point will  be (-1 , 1)

so
x = -1 and y = 1
put x and y in 5x+3y+2=0 

then
5(-1)+3(1)+2
-5 + 3 + 2
-5 +5
= 0
it means that it passes the line