Lesson straight line

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About ASHISHCRAB: I AM B.S(MATHEMATICS) PASSOUT SCIENCE BACKGROUND I CHALLANGE TO SOLVE ANY QUESTION RELATED ABOUT CO ORDINATE GEOMETRY

1. The straight lines x+ y =0, 3x+ y =4, x+3y-4=0 form a triangle which is
a) isosceles b) equilateral c). right angled d) none of these

2. The image of the point  -1, 3 ), by the line   x - y =0 is
a) (3,-1 ) b)  (1 , -3 ) c)  (-1 , -1 ) d)  (3 ,3 )

3. The equations of perpendicular bisectors of the sides AB and AC of a triangle ABC are  x-y+5=0 and x+2y=0
respectively. If the  point A is  (1, -2 ), the equation of the line BC is
a) 23 x +14 y  - 40 =0 b) 23x +14y + 40 = 0
c) 14 x +23y - 40 = 0 d) 14  x +23 y + 40 = 0

4. The equation of a line which passes through  (a cos ?, a sin ?) and perpendicular to the line
xsec? +y cosec ? =a is
a) x cos ? + y sin ? = 2 a cos 2? b) x sin ? - y cos  ?= 2 a sin 2?
c) x sin ? + y cos ? = 2 a cos 2? d) None of these.

7. Two sides  of an isosceles triangle are given by  the equation 7x- y+3=0 and x+ y-3=0. If its third
side  passes through the point (1, -10 ), then its equations are
a) x-3y-7 =0 or 3x+ y-31=0 b) x-3y-31=0 or 3x+ y-7=0
c) x-3y-31=0 or 3x+ y+7 =0 d) None of these.

9. The equations of the lines on which the perpendiculars from the origin make 30 angle with x - axis and which
form a triangle of area   with axes, are
50 / 3
a) x+ 3y �10 = 0 b) 3x+ y �10 = 0 c) x� 3y -10 = 0 d) None of these

10. The larger of the two angles made with x- axis of a straight line drawn through  1 , 2  so that it intersect x + y
6
= 4 at a distance  from  1 , 2 ) is
3
a) 105� b) 75� c) 60� d) 15�

11. The equation  of the line passing  through the intersection  of the line x-3y+1= 0 and 2x+5y-9 = 0
and at distance   from the origin is
5
a) 2x- y =5 b) x+2y =5 c) 2x+ y =5 d) x+2y =1

12. The line   x + y =4  divides the line joining  -1 , 1  and   ( 5 , 7 ) in the ratio ? :1, then the value of ?  is
1
a) 2 b) c) 3 d) None of these
2

13. In a rhombus ABCD, the diagonals AC and BD intersect at the point  3 , 4 . If the point A is
(1 ,2 ), the diagonal BD has the equation.
a) x- y-1= 0 b) x+ y-1= 0
c) x- y+1= 0 d) x+ y-7 = 0

14. If the straight line ax + by + c = 0 and xcosa+ysin a=c,enclose an angle p / 4 between them and meet the
straight line x sin a-y cos a =0 in the same point ,then
2 2 2 2 2
a) a +b =c b) a +b = 2
2 2 2 2 2
c) a +b =2c d) a +b = 4

15.      If each of the points (x1,4) and (-2, y1) lies on the line joining the points   (2 , -1 )  and  (5 , - 3 ), then the point
P(x , y1) lies on the line
1
a) x =3y b) x = -3y c) y = 2x+1 d) 2x+6y+1= 0.

16. The ratio in which the line  3x+4y+2 = 0 divides the distance between  3x+4y+5= 0  and
3x+4y-5 = 0 is
a) 7 : 3 b) 3 : 7 c) 2 : 3 d) None of these

17. If the extremities of the base of an isosceles triangle are the points  (2a, 0 ) and ( 0, a) and the equation of one
of the sides is x = 2a, then the area of the triangle is
a) 5 sq.units b) 5 / 2 sq. units c) 25 / 2 sq. units d) None of these.

18. The line 3x+2y = 24 meets y- axis at A and x- axis at B. The perpendicular bisector of AB meets the line
through  (0, -1 ) parallel to  x- axis at C. Then area of the triangle  ABC is
a) 182 sq. units b) 91 sq.units
c) 48 sq. units d) None of these.