Question

Find the location of the points (2, 2) and (3, 5) with respect to the line (i) 2x + 3y + 4 = 0 (ii) 3x – 2y + 2 = 0 (iii) x + y – 7 = 0

Answer 1

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Answer 2

Given:

Lines-(i) 2x + 3y + 4 = 0 (ii) 3x – 2y + 2 = 0 (iii) x + y – 7 = 0

To find:

location of the points (2, 2) and (3, 5)

Solution:

(i)Let the given line be P(x,y)=2x+3y+4

  Now, first put the (2,2) in the above eqaution

so, P(2,2)=2(2) + 3(2) + 4

              =4+6+4

               =14

Now, by putting the point(3,5) in the above equation, we will get

P(3,5)=2(3)+3(5)+4

         =6+15+4

          =25

Here,  the values obtained after putting the points in the line are not zero and both are of the same sign. Hence, the point lies on the same side of the line.

(ii) Let the given line be Q(x,y)=3x-2y+2-----(2)

   Putting (2,2) in (2)

  Q(2,2)=3(2) -2(2)+2

         =(6-4)+2=4

   Putting (3,5) in (2)

Q(3,5)=3(3) -2(5)+2

         =9-10+2= -1

Here,  the values obtained after putting the points in the line are of different signs. Hence, both the point lies on the opposite side of the line.

(iii)Let the given line be R(x,y)=x+y-7---->(3)

   Putting(2,2) in (3)

   R(2,2)=(2+2)-7

            =4-7= -3

  Putting (3,5) in (3)

 R(3,5)=3+5-7

           =1

Here,  the values obtained after putting the points in the line are of different signs. Hence, both the point lies on the opposite side of the line.