Question

1. Find the equation of the line parallel
to 2x+5y-9=0 and passing through the mid-point of the line segment joining
A=(2,7) and B=(-4,1).
 2. Write down the equation of the line
passing through (3,2) and perpendicular to the line 2y=3x+5
 3. Find the equation of the line whose
x-intercept is -3 an dis perpendicular to 3x+5y=1


4. Find the equation of the line
passing through (2,4) and perpendicular to x-axis
 5. Find the equation of the line whose
x and y-intercepts are given below:         a)
2,3 b) -2,4 ; c) 3,-2
 6. Change the equation 2x-3y-7=0 into
the intercept form.
 7. Is the line through (-2,3) and (4,1)
perpendicular to the line 3x=y+1? Does the line 3x=y+1 bisect the join of
(-2,3) and (4,1)?

8. Find the slopes of the following
lines. i) 2x-3y=8 ; ii) 2x+y=x+1 ; iii) 3x-4y+7=0; iv) x/a+y/b=1

Answer 1

1) equation of line parallel to given line : 2 x + 5 y + c =0Midpoint of A and B =   (2-4)/2 , (7+1)/2   = (-1, 4)

So -2 +20 +c = 0    c = -18
answer 2x + 5y = 18

2)
   equation of line perpendicular to given line 3y = -2x + c
      it passes thru  3,2                3*2 = -2 * 3 + c    =>   c = 12
             answer    3y +2x = 12

3)  
     equation line perpendicular to given line  5x - 3y = c
             put (-3,0):     (5*-3) - 3*0 = c        c = -15    
                       line is 5x - 3y + 15 =0

4)
               x = c              c = 2          so x = 2 is the answer


7)
       yes. 
               yes

8)  
       2/3    
        -1      
      3/4      
    -b/a