Question

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

Answer 1

first of all find mid point and then put that point in given equation

Answer 2

Answer:

Given Points : (2,0) and (0,2/9)

Find the mid point of given points

Formula : $x=\frac{x_1+x_2}{2} , y =\frac{y_1+y_2}{2}$

$(x_1,y_1)=(2,0)$

$(x_2,y_2)=(0,\frac{2}{9})$

Substitute the values

$x=\frac{2+0}{2} , y =\frac{0+\frac{2}{9}}{2}$

$x=1 , y =\frac{1}{9}$

we are given that (1, p/3) is the mid point of the line segment joining the ponits (2,0) and (0,2/9)

So, $(1,\frac{1}{9})=(1,\frac{p}{3}$

On comparing

$\frac{1}{9}=\frac{p}{3}$

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

$\frac{1}{3}=p$

Now we are supposed to find hat the line 5x +3y+2=0 passes through the point (-1,3p)

$(-1,3p)=(-1,3\times \frac{1}{3})$

$(-1,3p)=(-1,1)$

Substitute the point in line equation 5x +3y+2=0

$5x +3y+2=0$

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

$0=0$

Hence satisfied

So, the line 5x +3y+2=0 passes through the point (-1,3p)