Question

If P is (1, 2) and the line mirror is 2x – y + 4 = 0, find the coordinates of its image (i.e., Q).

Solution

Correct option is

Let the coordinates of Q be (x2y2).

The mid-point of PQ lies on 2x – y + 4 = 0  

  

Also the line PQ is perpendicular to the line mirror.  

  

Solving (i) and (ii), we get

    

SIMILAR QUESTIONS

Q1

Find the value of k so that the straight line 2x + 3y + 4 + k (6x – y + 12) = 0 and 7x + 5y – 4 = 0 are perpendicular to each other.

Q2

Show that the lines 2x – y – 12 = 0 and 3x + y – 8 = 0 intersect at a points which is equidistant from both the coordinates areas.

Q3

Find the area of triangle formed by the lines x – y + 1 = 0, 2x + y + 4 = 0 and x + 3 = 0.  

Q4

The line x + λy – 4 = 0 passes through the point of intersection of 4x – y+ 1 = 0 and x + y + 1 = 0. Find the values of λ.

Q5

Find the equation of a line parallel to x + 2y = 3 and passing through the point (3, 4).

Q6

Find the equation of the line perpendicular to 2x – 3y = 5 and cutting off an intercept 1 on the x-axis

Q7

Find the equation of the straight line passing through (2, –9) and the point of intersection of lines 2x + 5y – 8 = 0,

3x – 4y – 35 = 0  

Q8

Find the equation of straight line passing through the point of intersection of lines 3x – 4y +1 = 0, 5x + y – 1 = 0 and cutting off equal intercepts from coordinate axes.

Q9

Find the distance between the lines 5x + 12y + 40 = 0 and 10x + 24y – 25 = 0.

 

Q10

Find the values of λ for which the point (2 – λ, 1 + 2λ) lies on the non-origin side of the line 4x – y – 2 = 0.