Find the value of p so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.

 ncert cbse chapter 10 straight lines miscellaneous exercise 

 

9. Find the value of p so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and
2x – y – 3 = 0 may intersect at one point.

Consider the equation not containing p

3x + y = 2

2x - y =3

solving

adding  the

5x  = 5

x=1

re substitute in 3x+ y = 2

3(1) + y =2

y = 2-3 = (-1)

point of concurrency is (1,-1)

this should satisfy px + 2 y – 3 = 0

so p -2 -3 = 0

p=5

 

17. The hypotenuse of a right angled triangle has its ends at the points (1, 3) and
(– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle 

There are many such right angled triangles which can be found by taking points on the circumference of the circle with (1, 3) and (– 4, 1) as  ends of a diameter.

Of these, one of the easiest pair to identify 

is to plot the points (1, 3) and (– 4, 1)

and take a line  through (1,3)  parallel to the y axis  which gives x=1

and another perpendicular line through (-4,1) parallel to x axis which 

gives y=1.

 

or vice versa which gives x = (-4)  and y=3

ncert cbse chapter 10 straight lines miscellaneous exercise

24.  A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

solution

 

22. A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.

 

solution 

 21. Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 =0

solution

 

19. If the lines y = 3x +1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.

solution

18.Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the line to be a plane mirror.

solution 

 

17. The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle 

 solution

 

12.Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes

solution

 

11. Find the equation of the lines through the point (3, 2) which make an angle of 45 degrees with the line x – 2y = 3.

solution

 

8. Find the area of the triangle formed by the lines y – x = 0, x + y = 0 

and x – k = 0

solution

9. Find the value of p so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and
2x – y – 3 = 0 may intersect at one point.

 solution

 

ncert cbse chapter 9 sequences and series miscellaneous exercise

 

 32.

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on the second day. 4 more workers dropped out on the third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was finished

solution

 

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