Question

The line joining the points A(2, 0) and B(3, 1) is rotated about A in the anticlockwise direction through an angle of 15o. Find the equation of the line in the new position. If B goes to C in the new position, what will be the coordinates of C 

Solution

Correct option is

 

(By special corollary (i))

Here

     .         

and slope of, 

      

Now line AB is rotated through an angle of 15o

    

Equation of line AC in parametric form is  

        

  

  

     

        

and, 

      

         

Equation of the line AC is  

      

  

and coordinates of C are, 

      

 

Alternative Method (By special corollary (ii))

   

     

             

  

            

            

  

and equation of AC

       

.

SIMILAR QUESTIONS

Q1

 

Find the equation to the straight line which passes through the points (3, 4) and having intercepts on the axes: 

1. equal in magnitude but opposite in sign 

2. such that their sum is 14

Q2

Find the equation of the straight line through the point P(ab) parallel to the lines . Also find the intercepts made by it on the axes.

Q3

The length of perpendicular from the origin to a line is 9 and the line makes an angle of 120o with the positive direction of y-axis. Find the equation of the line.

Q4

Find the equation of the straight line on which the perpendicular from origin makes an angle of 30o with x-axis and which forms a triangle of area  sq. units with the coordinates axes.

Q5

Find the measure of the angle of intersection of the lines whose equations are 3x + 4y + 7 = 0 and 4x – 3y + 5 = 0.

Q6

 

Find the angle between the lines

                                                                     

where a > b > 0.

Q7

The slope of a straight line through A(3, 2) is 3/4. Find the coordinates of the points on the line that are 5 units away from A

Q8

 

Find the direction in which a straight line must be drawn through the point (1, 2) so that its point of intersection with the line

x + y = 4 may be at a distance  from this point. 

Q9

Find the distance of the point (2, 3) from the line 2x – 3y + 9 = 0 measured along the line 2x – 2y + 5 = 0.

Q10

The centre of a square is at the origin and one vertex is A(2, 1). Find the coordinates of other vertices of the square.