Question

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

Answer 1

Coordinates of the mid point X on the line joining of the points A and B are:

X= [( x1+x2)/2 ,( y1+y2)/2 ] ( midpoint Formula)

Since (1,p/3) is the midpoint of the line segment joining the points (2,0) & (0,2/9)

Here,
x= 1, y= p/3 , x1= 2, y1= 0 , x2= 0 , y2= 2/9

y= (y1+y2)/2

p/3=( 0+2/9)/2

p/3= (2/9)/2

2p =( 2/9)× 3

p = 3/9

p = ⅓

Given : (-1,3p)

x= -1 , y= 3p

y= 3× ⅓

y = 1

5x+3y+2=0. (Given)

Put the value of x & y

5 (-1) + 3(1)+2= 0

-5+3+2= 0

-2+2= 0

Hence, The line 5x + 3y + 2 = 0 passes through the point (–1, 1) as 5(–1) + 3(1) + 2 = 0.

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