Question

1. Prove that the points (-4,-6),
(1,3/2) and (2,3) do not form a triangle.


2. If the point (m,n) is equidistant
from the points (a-b, a+b) and (a+b,b-a) show that bm=an.


3. Show that the line joining the
points (4,3) and (8,6) passes through the origin.
 4. If A= (5,4) , B= (-3,-2) and
C=(1,-8) are the vertices of triangle ABC, find i) the slope of the median AD ;
ii) The slope of the altitude BM


5. Find the equation of the line i)
Parallel to the line 3x+2y=8 and passing through the point (0,1); ii) Parallel
to the line 7x-2y+8=0 and passing through (5,1); iii) Passing through the
origin and parallel to the line 3x-2y+1=0

Answer 1

1.
   Slope of AC = 9/6  = 3/2       slope of BC = (3/2 )/ 1   they are parallel

2.
      A(m,n)  B(a-b ,a+b)   C(a+b, b-a)
        Mid point D of BC  = (a, b)
            slope of AD = (b-n)/(a-m)       slope of BC = -2a/2b = -a/b
                 (b-n) / (a-m) = b/a    =>     mb =  an

3)
      slope of OA = 3/4        slope of OB = 6/8 = 3/4   So O is on line AB