STRAIGHT LINE

1. The medians BE and AD of a triangle
   with vertices A(0, b), B(0, 0) and C(a, 0)
   are perpendicular to each other, if:

(a) a=^ (b) b=^ (c) ab= 1 (d) a= ± √

2. The length of altitude through A of
   the triangle ABC, where A (-3, 0); B 
   (4, -1); C  (5, 2), is:

(a) √^ (b) √^ (c) √^ (d) √^

3. If the distance of any point P from
   the points A(a + b, a – b) and B(a – b, a

• b) are equal, then the locus of P is:
  (a) x – y= 0 (b) ax + by= 0 (c) bx – ay=
  0 (d) x + y= 0

4. If the area of the triangle with
   vertices (x, 0), (1, 1) and (0, 2) is 4
   square units, then the value of x is:
   (a) -2 (b) -4 (c) -6 (d) 8


5. Three vertices of a parallelogram
   taken in order are (-1, -6), (2, -5) and
   (7, 2). The fourth vertex is:
   (a) (1, 4) (b) (4, 1) (c) (1, 1) (d) (4, 4)


6. If A, B, C, D are four points in a
   straight line such that distance from A
   to B is 10, B to C is 5, C to D is 4 and A
   to D is 1, then their correct sequence is:
   (a) A – B – C – D (b) C – D – A – B

(c) A – D – C – B (d) C – B – A – D

7. The Cartesian equation of the curve
   x= 5 + 3 cos α and y= 7 + 3 sin α is
   represented by:
   (a) ( )^ ( )^ (b)

( )^ ( )^ (c) y= 3x + 7

(d) (y – 2) + (x – 7)= 5

8. If the points with co-ordinates (-a, 0),
   ( ) and ( ) are
   collinear, then the value of is:
   (a) 3 (b) 2 (c) 1 (d) - 1


9. If the vertices B and D of a square
   ABCD be (2, 3) and (4, 1) respectively,
   then the length of its side is:
   (a) 1 unit (b) 2 unit (c) 3 unit (d) 4
   unit


10. The middle point of A(1, 2) and B(x,
    y) is C(2, 4). If BD is perpendicular to
    AB such that CD= 3 units, then what is
    the length BD?
    (a) 2√ units (b) 2 units (c) 3 units
    (d) 3√ units


11. If the points A(1, 2), B(2, 4) and C(3,
    a) are collinear, what is the length BC?
    (a) √ units (b) √ units

(c) √ units (d) 5 units

12. The length of perpendicular from
    the point (a cos α, a sin α) upon the
    straight line y= x tan α + c, c > 0, is:
    (a) c (b) c α (c) c cos α (d) c α


13. In what ratio is the line y – x +2= 0
    divides the line joining the points (3, -

1. and (8, 9)?
   (a) 1 : 2 (b) 2 : 1 (c) 2 : 3 (d) 3 : 4

14. Equation of the straight line making
    equal intercepts on the axes and