Question

Mid point of line segment joining points (X1,Y1) and (X2,Y2) is( X1+X2/2,Y1+Y2/2). If C is the midpoint of the line segment AB then distance of C from A is equal to distance of C from B. point A(2,0) and point B(0,2/9). Point C(1,p/3). answer the following : a) find value of p. b) show that 5x+3y+2=0 passes through the point (-1,3p).​

Answer 1

Answer:

yes it is very easy and right answer

Answer 2

Given:

A line AB is given with point A(2,0) and point B (0,2/9). C is the midpoint on line AB with Points C(1,p/3).

To find:

a) Find the value of p.

b) Show that 5x+3y+2=0 passes through the point (-1,3p).

Step-by-step explanation:

• According to question C is the midpoint of line AB.

             A(2,0)  ---------------------------------------------------  B(0,2/9)

                                             C(1,p/3)

• Coordinates of midpoint C can be calculated by

        $C(x,y)=\frac{X_1+X_2}{2},\frac{Y_1+Y_2}{2}$

        $C(x,y)=[\frac{2+0}{2} ],[\frac{2/9}{2} ]$

        $C(x,y)=[\frac{2+0}{2} ],[\frac{2/9}{2} ]$

• Compare the coordinates of point C with given points.

      $(1,p/3) = (1,1/9)$

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

   So, value of p is 1/3.

• Check wether 5x+3y+2=0 passes through the point (-1,3p)

        First put the value of p in the co-ordinate.

        point (-1,1)

• Now, put the coordinates in the equation 5x+3y+2=0

          $5(-1)+3(1)+2=0$

                                  $0=0$

                           L.H.S = R.H.S

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