Question

Find the orthocentre of the triangle of the triangle ABC whose angular points are A(1, 2), B(2, 3) and C(4, 3).  

Solution

Correct option is

(1, 6)

 

Now, 

                                 

       

and, 

         

Let orthocentre be O’(α, β) then 

    slope of OA × slope of BC = –1   

             

  

  

  

and     slope of OB × slope of CA = –1   

  

  

  

Hence orthocentre of the given triangle is (1, 6).

SIMILAR QUESTIONS

Q1

If p and p’ are the length of the perpendiculars from the origin to the straight line whose equations are , then find the value of 4p2 + p2.

Q2

 

Find the distance between the lines 5x – 12y + 2 = 0 and

 5x – 12y – 3 = 0.

Q3

Find the equations of the line parallel to 5x – 12y + 26 = 0 and at a distance of 4 units from it.

Q4

If the lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0 (ab and cbeing distinct and difference from 1) are concurrent, then find the value of

Q5

Find the equation of the straight line passing through the point (2, 1) and through the point of intersecction of the lines x + 2y = 3 and 2x – 3y = 4.

Q6

The family of lines x(a + 2b) + y(+ 3b) = b passes through the point for all values of a and b. Find the point.

Q7

If 3a + 2b + 6c = 0 the family of straight lines ax + by + c = 0 passes through a fixed point. Find the coordinates of fixed point.

Q8

 

Find the equation of the line passing through the point of intersection of the lines

          x + 5y + 7 = 0, 3x + 2y – 5 = 0 and   

1. parallel to the line 7x + 2y – 5 = 0

2. perpendicular to the line 7x + 2y – 5 = 0

Q9

 

Find the equation of straight line which passes through the intersection of the straight lines  

        3x – 4y + 1 = 0 and 5x + y – 1 = 0 

and cuts off equal intercepts from the axes.

Q10

 

If the orthocentre of the triangle formed by the lines

2x + 3y – 1 = 0, x + 2y – 1 = 0, ax + by – 1 = 0   is at origin, then find (a,b).