Question

If the algebraic sum of the perpendicular distances of a variable line from the points (0, 2), (2, 0) and (1, 1) is zero, then the line always passes through the point

Solution

Correct option is

(1, 1)

If the line be ax + by + c = 0,

  

  

⇒  the line ax + by + c = 0 always passes through the point (1, 1).

       

SIMILAR QUESTIONS

Q1

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

 

Q2

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

Q3

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. 

Q4

Find the incentre of ΔABC if A is (4, –2), B is (–2, 4) and C is (5, 5).

Q5

Find the coordinates of the orthcentre of the triangle whose vertices are (0, 0), (2, –1) and (–1, 3).

Q6

Find straight lines represented by 6x2 + 13xy + 6y2 + 8x + 7y + 2 = 0 and also find the point of intersection.  

Q7

If abc are all distinct, then the equations (b – c)x + (c – a)y + a – b = 0 and (b3 – c3)x + (c3 – a3)y + a3 – b3 = 0 represent the same line if

Q8

If the pair of lines x2 – 2pxy – y2 = 0 and x2 – 2qxy – y2 = 0 are such that each pair bisects the angle between the other pair, then pq equals  

Q9

Angles made with x-axis by the two lines through the point  (1, 2) and cutting the line x + y = 4 at a distance  from the point (1, 2) are

Q10

 be three points. Then the equation of the bisector of angle PQR is