# Straight Lines

```AHLCON PUBLIC SCHOOL
Class : XI - MATHEMATICS
Assignment – 10 (2014 – 2015)
Chapter : Straight Lines
Questions:
1. Find the equation of the line which satisfies the given conditions.
a. Passing through the point  1,2 with slope 4.


2 ,2 2, with slope 2 3 .
c. Passing through the point 2,2 and inclined to x – axis at 45o.
b. Passing through the point
d. Intersecting x – axis at a distance of 4 units to the right of origin with slope – 1.
e. Passing through the points 0,3 and 5,0 .
2. Find the equation of the right bisectors of the line segment joining the points A1,0 and B2,3 .
3. Find the equations of medians of triangle ABC whose vertices are A 1,6 , B 3,9 , C5,8 .
4. Find the equations of the sides of the triangle whose vertices are 2,1,  2,3, 4,3.
5. The points A1,3 and C 6,8 are the two opposite vertices of the square ABCD. Find the equations
of the diagonal BD.
6. ABCD is a rectangle. The points A and C are  3,1 and 1,1 respectively. Equation AB is
4 x  7 y  5  0 . Find the equation of other three sides.
7. The base of an equilateral triangle is x – axis and the vertex is 0,4 . Find the equation of other two
sides.
8. The area of the triangle formed by co-ordinate axes and a line is 6 sq. units and the length of
hypotenuse is 54m. Find the equation of the line.
9. Find the equation of a line which passes through 12,2 and is such that the intercept on x – axis
exceeds the intercept on y – axis by 4 units.
10. Reduce the following equations into slope intercept form:
a) 3 x  3 y  5
b) 7 x  3 y  6  0
11. Reduce each of the following to the normal form and find the length of perpendicular from origin to
the line.
1.
2.
x y20
4x  3y  9  0
12. Reduce the following equations to intercept form and find the intercepts on the axes.
i.
ii.
3x  y  2  0
3 x  4 y  12
13. Find the coordinates of the ortho-centre of the triangle whose vertices are 1,3, 2,3 and 0,0 .
14. Find the angle between the lines y  3 x  5  0 and
3y  x  6  0 .
15. A vertex of an equilateral triangle is 2,3 and the equation of the opposite side is
the equation of other two sides.
3 x  y  2. Find
16. Determine the distance between pair of lines in each case.
a) 4 x  3 y  9  0 and 4 x  3 y  24  0
b) 9 x  40 y  20 and 9 x  40 y  103  0
17. Find the equations of the lines which pass to the point 4,5 and made equal angles with the lines
5 x  12 y  6  0 and 3 x  4 y  7 .
18. Two lines cut the x – axis at distances 4 and -4 and the y – axis at distances 2 and 6 respectively from
the origin. Find the co-ordinates of their point of intersection.
19. A lines forms a triangle with co-ordinate axis. If the area of the triangle is 54 3 square units and
perpendicular drawn from the origin to the line makes an angle of 60 degree with x – axis. Find the
equation of the line.
20. Prove that the diagonals of the parallelogram formed by the lines
3 x  y  0, 3 y  x  0, 3 x  y  1, 3 y  x  1 are at right angle to each other.
21. Find the equation of the line through the intersection of 5 x  3 y  1 and 2 x  3 y  23  0 and
perpendicular to the line 5 x  3 y  1  0 .
22. Find the equation of the line through the intersection of x  2 y  3  0 and 4 x  y  7  0 and
which is parallel to 5 x  4 y  20  0
23. The points 1,3 and 5,1 are the opposite vertices of rectangle. The other two vertices lie on
y  2 x  c . Find the c and the other vertices.
24. Find the equation of the line through the point 3,2 which makes an angle of 45degree with
x  2y  3.
25. One side of a square is inclined to the x – axis at an angle  and one of the extremities is at the
origin. If the side of square is 4 find the equation of the diagonals of the square.
26. Find the point on the line x  2 y  3 whose distance from 3x  4 y  2  0 is 2.
27. A ray of light passing through the point 4,5 and reflects on the x – axis at a point 3,0 . Find the
equation of the reflected ray.
28. Prove that the line 5 x  2 y  1  0 is mid parallel to the lines 5 x  2 y  9  0 and 5 x  2 y  7  0 .
29. If the origin be shifted to the point 2,3 by a transaction of coordinate axes. Find the new
coordinates of point 4,7  .
30. If the origin be shifted to the point 3,1 . Find the new equation of the line 2 x  3 y  5  0
31. Find the point to which the origin be shifted after a translation, so that the equation
x 2  y 2  4 x  8 y  3  0 will have no first degree form.
32. Transform the equations 2 x 2  y 2  4 x  4 y  0 to parallel axes when the origin is shifted to the
point 1,2
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