Question

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

Answer 1

Midpoint of line segment joining (0,2) and (0,2/9) will be (x,y)

Therefore,

$x = \frac{x1 + x2}{2}$


$y = \frac{y1 + y2}{2}$


Now in question we have already given that
x = 1 and y = p/3. So to find value of p we have to use equation of y. i.e.


$\frac{p}{3} = \frac{y1 + y2}{2}$


$\frac{p}{3} = \frac{2 + \frac{2}{9} }{2}$


$\frac{p}{3} = \frac{ \frac{18 + 2}{9} }{2}$


$\frac{p}{3} = \frac{ 20 }{18}$


$p = \frac{20 \times 3}{18}$


$p = \frac{10}{3}$


So we get value of p. Now put it in (-1,3p)
We will get (-1,10)

So Now we have to prove that 5x+3y+2=0 is passing through (-1,10)

So put this point in equation of line.

$5( - 1) + 3(10) + 2 = 0$
But -5+32 ≠ 0

So point (-1,3p) where p = 10/3 does not lies on line 5x+3y+2=0