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

Answer 1

ince p 1, 3 is the mid-point of the line segment joining the points (2, 0) and 2 0, 9

herefore, 2 0 p 1 9 p 3 2 3

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

Answer 2

Answer:

The value of p is 1/3.

Step-by-step explanation:

It is given that (1,p/3) is the mid point of the line segment joining the points (2,0) and (0,2/9).

The midpoint formula:

$Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$(1,\frac{p}{3})=(\frac{2+0}{2},\frac{0+\frac{2}{9}}{2})$

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

On comparing both the sides,

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

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

The value of p is 1/3.

The coordinates of point (-1,3p) are

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

Put these points in equation 5x+3y+2=0.

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

$-5+3+2=0$

$0=0$

Since LHS=RHS, therefore the point (-1,3p) passing through the line 5x+3y+2=0. Hence proved.